Propagation And Interaction Of Singularities In Nonlinear Hyperbolic Problems

Download Propagation And Interaction Of Singularities In Nonlinear Hyperbolic Problems full books in PDF, epub, and Kindle. Read online Propagation And Interaction Of Singularities In Nonlinear Hyperbolic Problems ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems

Author : Michael Beals
Publisher : Springer Science & Business Media
ISBN 13 : 1461245540
Total Pages : 153 pages
Book Rating : 4.4/5 (612 download)

DOWNLOAD NOW!

Book Synopsis Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems by : Michael Beals

Download or read book Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems written by Michael Beals and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book developed from a series of lectures I gave at the Symposium on Nonlinear Microlocal Analysis held at Nanjing University in October. 1988. Its purpose is to give an overview of the use of microlocal analysis and commutators in the study of solutions to nonlinear wave equations. The weak singularities in the solutions to such equations behave up to a certain extent like those present in the linear case: they propagate along the null bicharacteristics of the operator. On the other hand. examples exhibiting singularities not present in the linear case can also be constructed. I have tried to present a crossection of both the regularity results and the singular examples. for problems on the interior of a domain and on domains with boundary. The main emphasis is on the case of more than one space dimen sion. since that case is treated in great detail in the paper of Rauch-Reed 159]. The results presented here have for the most part appeared elsewhere. and are the work of many authors. but a few new examples and proofs are given. I have attempted to indicate the essential ideas behind the arguments. so that only some of the results are proved in full detail. It is hoped that the central notions of the more technical proofs appearing in research papers will be illuminated by these simpler cases.

Nonlinear Hyperbolic Equations and Field Theory

Author : M K V Murthy
Publisher : CRC Press
ISBN 13 : 9780582087668
Total Pages : 242 pages
Book Rating : 4.0/5 (876 download)

DOWNLOAD NOW!

Book Synopsis Nonlinear Hyperbolic Equations and Field Theory by : M K V Murthy

Download or read book Nonlinear Hyperbolic Equations and Field Theory written by M K V Murthy and published by CRC Press. This book was released on 1992-03-30 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of a workshop on nonlinear hyperbolic equations held at Varenna, Italy in June 1990.

Symbolic Calculus Semilinear Hyperbolic Progressing Waves

Author : Hassane Bougrini
Publisher : Nova Publishers
ISBN 13 : 9781560728788
Total Pages : 122 pages
Book Rating : 4.7/5 (287 download)

DOWNLOAD NOW!

Book Synopsis Symbolic Calculus Semilinear Hyperbolic Progressing Waves by : Hassane Bougrini

Download or read book Symbolic Calculus Semilinear Hyperbolic Progressing Waves written by Hassane Bougrini and published by Nova Publishers. This book was released on 2000 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this book is to give a self-contained synthesis of different results in the domain of symbolic calculus of conormal singularities of semilinear hyperbolic progressing waves. The authors deal generally with real matrix valued co-efficients and with real vector valued solutions, but the complex case is similar. They consider also N x N first order systems rather than high order scalar equations, because the polarisation properties of symbols are less natural in the latter case. Moreover, although they assume generally that the real characteristics are simple, the methods can give results for symmetric or symmetrisable first order hyperbolic systems.

Analysis of Singularities for Partial Differential Equations

Author :
Publisher :
ISBN 13 : 9814464996
Total Pages : pages
Book Rating : 4.8/5 (144 download)

DOWNLOAD NOW!

Book Synopsis Analysis of Singularities for Partial Differential Equations by :

Download or read book Analysis of Singularities for Partial Differential Equations written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Wave Equations

Author : Satyanad Kichenassamy
Publisher : CRC Press
ISBN 13 : 1000444724
Total Pages : 297 pages
Book Rating : 4.0/5 (4 download)

DOWNLOAD NOW!

Book Synopsis Nonlinear Wave Equations by : Satyanad Kichenassamy

Download or read book Nonlinear Wave Equations written by Satyanad Kichenassamy and published by CRC Press. This book was released on 2021-05-30 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work examines the mathematical aspects of nonlinear wave propagation, emphasizing nonlinear hyperbolic problems. It introduces the tools that are most effective for exploring the problems of local and global existence, singularity formation, and large-time behaviour of solutions, and for the study of perturbation methods.

Partial Differential Equations III

Author : Michael Taylor
Publisher : Springer Science & Business Media
ISBN 13 : 1475741901
Total Pages : 629 pages
Book Rating : 4.4/5 (757 download)

DOWNLOAD NOW!

Book Synopsis Partial Differential Equations III by : Michael Taylor

Download or read book Partial Differential Equations III written by Michael Taylor and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L Sobolev spaces, H lder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is aimed at graduate students in mathematics, and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis and complex analysis. ^

F.B.I. Transformation

Author : Jean-Marc Delort
Publisher : Springer
ISBN 13 : 366221539X
Total Pages : 108 pages
Book Rating : 4.6/5 (622 download)

DOWNLOAD NOW!

Book Synopsis F.B.I. Transformation by : Jean-Marc Delort

Download or read book F.B.I. Transformation written by Jean-Marc Delort and published by Springer. This book was released on 2013-12-11 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last ten years, FBI transformation and second microlocalization have been used by several authors to solve different problems in the theory of linear or nonlinear partial differential equations. The aim of this book is to give an introduction to these topics, in the spirit of the work ofSj strand, and to present their recent application to the propagation of conormal singularities for solutions of seminlinear hyperbolic equations, due to Lebeau. The text is quite self-contained and provides a useful entry to the subject and a bridging link to more specialized papers.

Quantization, Nonlinear Partial Differential Equations, and Operator Algebra

Author : John Von Neumann
Publisher : American Mathematical Soc.
ISBN 13 : 0821803816
Total Pages : 224 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Quantization, Nonlinear Partial Differential Equations, and Operator Algebra by : John Von Neumann

Download or read book Quantization, Nonlinear Partial Differential Equations, and Operator Algebra written by John Von Neumann and published by American Mathematical Soc.. This book was released on 1996 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent inroads in higher-dimensional nonlinear quantum field theory and in the global theory of relevant nonlinear wave equations have been accompanied by very interesting cognate developments. These developments include symplectic quantization theory on manifolds and in group representations, the operator algebraic implementation of quantum dynamics, and differential geometric, general relativistic, and purely algebraic aspects. Quantization and Nonlinear Wave Equations thus was highly appropriate as the theme for the first John von Neumann Symposium (June 1994) held at MIT. The symposium was intended to treat topics of emerging signifigance underlying future mathematical developments. This book describes the outstanding recent progress in this important and challenging field and presents general background for the scientific context and specifics regarding key difficulties. Quantization is developed in the context of rigorous nonlinear quantum field theory in four dimensions and in connection with symplectic manifold theory and random Schrodinger operators. Nonlinear wave equations are exposed in relation to recent important progress in general relativity, in purely mathematical terms of microlocal analysis, and as represented by progress on the relativistic Boltzmann equation. Most of the developments in this volume appear in book form for the first time. The resulting work is a concise and informative way to explore the field and the spectrum of methods available for its investigation.

Proceedings of the Third Asian Mathematical Conference 2000

Author : Toshikazu Sunada
Publisher : World Scientific
ISBN 13 : 9810249470
Total Pages : 633 pages
Book Rating : 4.8/5 (12 download)

DOWNLOAD NOW!

Book Synopsis Proceedings of the Third Asian Mathematical Conference 2000 by : Toshikazu Sunada

Download or read book Proceedings of the Third Asian Mathematical Conference 2000 written by Toshikazu Sunada and published by World Scientific. This book was released on 2002 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: COntains 55 research and expository articles on a wide range of currently active and interesting areas in pure and applied mathematics.

Partial Differential Equations III

Author : Michael E. Taylor
Publisher : Springer Science & Business Media
ISBN 13 : 1441970495
Total Pages : 734 pages
Book Rating : 4.4/5 (419 download)

DOWNLOAD NOW!

Book Synopsis Partial Differential Equations III by : Michael E. Taylor

Download or read book Partial Differential Equations III written by Michael E. Taylor and published by Springer Science & Business Media. This book was released on 2010-11-02 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L Sobolev spaces, H lder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is aimed at graduate students in mathematics, and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis and complex analysis

Hyperbolic Partial Differential Equations and Geometric Optics

Author : Jeffrey Rauch
Publisher : American Mathematical Soc.
ISBN 13 : 0821872915
Total Pages : 386 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Hyperbolic Partial Differential Equations and Geometric Optics by : Jeffrey Rauch

Download or read book Hyperbolic Partial Differential Equations and Geometric Optics written by Jeffrey Rauch and published by American Mathematical Soc.. This book was released on 2012-05-01 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces graduate students and researchers in mathematics and the sciences to the multifaceted subject of the equations of hyperbolic type, which are used, in particular, to describe propagation of waves at finite speed. Among the topics carefully presented in the book are nonlinear geometric optics, the asymptotic analysis of short wavelength solutions, and nonlinear interaction of such waves. Studied in detail are the damping of waves, resonance, dispersive decay, and solutions to the compressible Euler equations with dense oscillations created by resonant interactions. Many fundamental results are presented for the first time in a textbook format. In addition to dense oscillations, these include the treatment of precise speed of propagation and the existence and stability questions for the three wave interaction equations. One of the strengths of this book is its careful motivation of ideas and proofs, showing how they evolve from related, simpler cases. This makes the book quite useful to both researchers and graduate students interested in hyperbolic partial differential equations. Numerous exercises encourage active participation of the reader. The author is a professor of mathematics at the University of Michigan. A recognized expert in partial differential equations, he has made important contributions to the transformation of three areas of hyperbolic partial differential equations: nonlinear microlocal analysis, the control of waves, and nonlinear geometric optics.

Periodic Solutions of Singular Lagrangian Systems

Author : A. Ambrosetti
Publisher : Springer Science & Business Media
ISBN 13 : 1461203198
Total Pages : 168 pages
Book Rating : 4.4/5 (612 download)

DOWNLOAD NOW!

Book Synopsis Periodic Solutions of Singular Lagrangian Systems by : A. Ambrosetti

Download or read book Periodic Solutions of Singular Lagrangian Systems written by A. Ambrosetti and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thismonographdealswiththeexistenceofperiodicmotionsof Lagrangiansystemswith ndegreesoffreedom ij + V'(q) =0, where Visasingularpotential. Aprototypeofsuchaproblem, evenifitisnottheonlyphysicallyinterestingone, istheKepler problem . q 0 q+yqr= . This, jointlywiththemoregeneralN-bodyproblem, hasalways beentheobjectofagreatdealofresearch. Mostofthoseresults arebasedonperturbationmethods, andmakeuseofthespecific featuresoftheKeplerpotential. OurapproachismoreonthelinesofNonlinearFunctional Analysis:ourmainpurposeistogiveafunctionalframefor systemswithsingularpotentials, includingtheKeplerandthe N-bodyproblemasparticularcases. PreciselyweuseCritical PointTheorytoobtainexistenceresults, qualitativeinnature, whichholdtrueforbroadclassesofpotentials. Thishighlights thatthevariationalmethods, whichhavebeenemployedtoob tainimportantadvancesinthestudyofregularHamiltonian systems, canbesuccessfallyusedtohandlesingularpotentials aswell. Theresearchonthistopicisstillinevolution, andtherefore theresultswewillpresentarenottobeintendedasthefinal ones. Indeedamajorpurposeofourdiscussionistopresent methodsandtoolswhichhavebeenusedinstudyingsuchprob lems. Vlll PREFACE Partofthematerialofthisvolumehasbeenpresentedina seriesoflecturesgivenbytheauthorsatSISSA, Trieste, whom wewouldliketothankfortheirhospitalityandsupport. We wishalsotothankUgoBessi, PaoloCaldiroli, FabioGiannoni, LouisJeanjean, LorenzoPisani, EnricoSerra, KazunakaTanaka, EnzoVitillaroforhelpfulsuggestions. May26,1993 Notation n 1. For x, yE IR, x. ydenotestheEuclideanScalarproduct, and IxltheEuclideannorm. 2. meas(A)denotestheLebesguemeasureofthesubset Aof n IR - 3. Wedenoteby ST =[0,T]/{a, T}theunitarycirclepara metrizedby t E[0,T]. Wewillalsowrite SI= ST=I. n 1 n 4. Wewillwrite sn = {xE IR + : Ixl =I}andn = IR \{O}. n 5. Wedenoteby LP([O, T], IR),1~ p~+00,theLebesgue spaces, equippedwiththestandardnorm lIulip. l n l n 6. H (ST, IR)denotestheSobolevspaceof u E H,2(0, T; IR) suchthat u(O) = u(T). Thenormin HIwillbedenoted by lIull2 = lIull~ + lIull~· 7. Wedenoteby(·1·)and11·11respectivelythescalarproduct andthenormoftheHilbertspace E. 8. For uE E, EHilbertorBanachspace, wedenotetheball ofcenter uandradiusrby B(u, r) = {vE E: lIu- vii~ r}. Wewillalsowrite B = B(O, r). r 1 1 9. WesetA (n) = {uE H (St, n)}. k 10. For VE C (1Rxil, IR)wedenoteby V'(t, x)thegradient of Vwithrespectto x. l 11. Given f E C (M, IR), MHilbertmanifold, welet r = {uEM: f(u) ~ a}, f-l(a, b) = {uE E : a~ f(u) ~ b}. x NOTATION 12. Given f E C1(M, JR), MHilbertmanifold, wewilldenote by Zthesetofcriticalpointsof fon Mandby Zctheset Z U f-l(c, c). 13. Givenasequence UnE E, EHilbertspace, by Un --"" Uwe willmeanthatthesequence Unconvergesweaklyto u. 14. With £(E)wewilldenotethesetoflinearandcontinuous operatorson E. 15. With Ck''''(A, JR)wewilldenotethesetoffunctions ffrom AtoJR, ktimesdifferentiablewhosek-derivativeisHolder continuousofexponent0:. Main Assumptions Wecollecthere, forthereader'sconvenience, themainassump tionsonthepotential Vusedthroughoutthebook. (VO) VEC1(lRXO, lR), V(t+T, x)=V(t, X) V(t, x)ElRXO, (VI) V(t, x)

Analytic Semigroups and Optimal Regularity in Parabolic Problems

Author : Alessandra Lunardi
Publisher : Springer Science & Business Media
ISBN 13 : 9783764351724
Total Pages : 452 pages
Book Rating : 4.3/5 (517 download)

DOWNLOAD NOW!

Book Synopsis Analytic Semigroups and Optimal Regularity in Parabolic Problems by : Alessandra Lunardi

Download or read book Analytic Semigroups and Optimal Regularity in Parabolic Problems written by Alessandra Lunardi and published by Springer Science & Business Media. This book was released on 1995-01-27 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be fruitfully applied to the study of parabolic problems. Particular attention is paid to optimal regularity results in linear equations. Furthermore, these results are used to study several other problems, especially fully nonlinear ones. Owing to the new unified approach chosen, known theorems are presented from a novel perspective and new results are derived. The book is self-contained. It is addressed to PhD students and researchers interested in abstract evolution equations and in parabolic partial differential equations and systems. It gives a comprehensive overview on the present state of the art in the field, teaching at the same time how to exploit its basic techniques. - - - This very interesting book provides a systematic treatment of the basic theory of analytic semigroups and abstract parabolic equations in general Banach spaces, and how this theory may be used in the study of parabolic partial differential equations; it takes into account the developments of the theory during the last fifteen years. (...) For instance, optimal regularity results are a typical feature of abstract parabolic equations; they are comprehensively studied in this book, and yield new and old regularity results for parabolic partial differential equations and systems. (Mathematical Reviews) Motivated by applications to fully nonlinear problems the approach is focused on classical solutions with continuous or Hölder continuous derivatives. (Zentralblatt MATH)

Surveys in Applied Mathematics

Author : Mark I. Freidlin
Publisher : Springer Science & Business Media
ISBN 13 : 1461519918
Total Pages : 297 pages
Book Rating : 4.4/5 (615 download)

DOWNLOAD NOW!

Book Synopsis Surveys in Applied Mathematics by : Mark I. Freidlin

Download or read book Surveys in Applied Mathematics written by Mark I. Freidlin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 2 offers three in-depth articles covering significant areas in applied mathematics research. Chapters feature numerous illustrations, extensive background material and technical details, and abundant examples. The authors analyze nonlinear front propagation for a large class of semilinear partial differential equations using probabilistic methods; examine wave localization phenomena in one-dimensional random media; and offer an extensive introduction to certain model equations for nonlinear wave phenomena.

Nonlinear Waves and Weak Turbulence

Author : FITZMAURICE
Publisher : Springer Science & Business Media
ISBN 13 : 1461203317
Total Pages : 354 pages
Book Rating : 4.4/5 (612 download)

DOWNLOAD NOW!

Book Synopsis Nonlinear Waves and Weak Turbulence by : FITZMAURICE

Download or read book Nonlinear Waves and Weak Turbulence written by FITZMAURICE and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an outgrowth of the NSF-CBMS conference Nonlinear Waves £3 Weak Turbulence held at Case Western Reserve University in May 1992. The principal speaker at the conference was Professor V. E. Zakharov who delivered a series of ten lectures outlining the historical and ongoing developments in the field. Some twenty other researchers also made presentations and it is their work which makes up the bulk of this text. Professor Zakharov's opening chapter serves as a general introduction to the other papers, which for the most part are concerned with the application of the theory in various fields. While the word "turbulence" is most often associated with f:l. uid dynamics it is in fact a dominant feature of most systems having a large or infinite number of degrees of freedom. For our purposes we might define turbulence as the chaotic behavior of systems having a large number of degrees of freedom and which are far from thermodynamic equilibrium. Work in field can be broadly divided into two areas: • The theory of the transition from smooth laminar motions to the disordered motions characteristic of turbulence. • Statistical studies of fully developed turbulent systems. In hydrodynamics, work on the transition question dates back to the end of the last century with pioneering contributions by Osborne Reynolds and Lord Rayleigh.

Topics in Nonlinear Analysis

Author : Joachim Escher
Publisher : Birkhäuser
ISBN 13 : 3034887655
Total Pages : 741 pages
Book Rating : 4.0/5 (348 download)

DOWNLOAD NOW!

Book Synopsis Topics in Nonlinear Analysis by : Joachim Escher

Download or read book Topics in Nonlinear Analysis written by Joachim Escher and published by Birkhäuser. This book was released on 2012-12-06 with total page 741 pages. Available in PDF, EPUB and Kindle. Book excerpt: Herbert Amann's work is distinguished and marked by great lucidity and deep mathematical understanding. The present collection of 31 research papers, written by highly distinguished and accomplished mathematicians, reflect his interest and lasting influence in various fields of analysis such as degree and fixed point theory, nonlinear elliptic boundary value problems, abstract evolutions equations, quasi-linear parabolic systems, fluid dynamics, Fourier analysis, and the theory of function spaces. Contributors are A. Ambrosetti, S. Angenent, W. Arendt, M. Badiale, T. Bartsch, Ph. Bénilan, Ph. Clément, E. Faöangová, M. Fila, D. de Figueiredo, G. Gripenberg, G. Da Prato, E.N. Dancer, D. Daners, E. DiBenedetto, D.J. Diller, J. Escher, G.P. Galdi, Y. Giga, T. Hagen, D.D. Hai, M. Hieber, H. Hofer, C. Imbusch, K. Ito, P. Krejcí, S.-O. Londen, A. Lunardi, T. Miyakawa, P. Quittner, J. Prüss, V.V. Pukhnachov, P.J. Rabier, P.H. Rabinowitz, M. Renardy, B. Scarpellini, B.J. Schmitt, K. Schmitt, G. Simonett, H. Sohr, V.A. Solonnikov, J. Sprekels, M. Struwe, H. Triebel, W. von Wahl, M. Wiegner, K. Wysocki, E. Zehnder and S. Zheng.

Nonlinear Diffusion Equations and Their Equilibrium States, 3

Author : N.G Lloyd
Publisher : Springer Science & Business Media
ISBN 13 : 1461203937
Total Pages : 567 pages
Book Rating : 4.4/5 (612 download)

DOWNLOAD NOW!

Book Synopsis Nonlinear Diffusion Equations and Their Equilibrium States, 3 by : N.G Lloyd

Download or read book Nonlinear Diffusion Equations and Their Equilibrium States, 3 written by N.G Lloyd and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear diffusion equations have held a prominent place in the theory of partial differential equations, both for the challenging and deep math ematical questions posed by such equations and the important role they play in many areas of science and technology. Examples of current inter est are biological and chemical pattern formation, semiconductor design, environmental problems such as solute transport in groundwater flow, phase transitions and combustion theory. Central to the theory is the equation Ut = ~cp(U) + f(u). Here ~ denotes the n-dimensional Laplacian, cp and f are given functions and the solution is defined on some domain n x [0, T] in space-time. FUn damental questions concern the existence, uniqueness and regularity of so lutions, the existence of interfaces or free boundaries, the question as to whether or not the solution can be continued for all time, the asymptotic behavior, both in time and space, and the development of singularities, for instance when the solution ceases to exist after finite time, either through extinction or through blow up.