Blow Up In Quasilinear Parabolic Equations

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Blow-Up in Quasilinear Parabolic Equations

Author : A. A. Samarskii
Publisher : Walter de Gruyter
ISBN 13 : 3110889862
Total Pages : 561 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Blow-Up in Quasilinear Parabolic Equations by : A. A. Samarskii

Download or read book Blow-Up in Quasilinear Parabolic Equations written by A. A. Samarskii and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Degenerate Parabolic Equations

Author : Emmanuele DiBenedetto
Publisher : Springer Science & Business Media
ISBN 13 : 1461208955
Total Pages : 402 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Degenerate Parabolic Equations by : Emmanuele DiBenedetto

Download or read book Degenerate Parabolic Equations written by Emmanuele DiBenedetto and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Evolved from the author's lectures at the University of Bonn's Institut für angewandte Mathematik, this book reviews recent progress toward understanding of the local structure of solutions of degenerate and singular parabolic partial differential equations.

Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations

Author : Victor A. Galaktionov
Publisher : CRC Press
ISBN 13 : 1482251736
Total Pages : 565 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations by : Victor A. Galaktionov

Download or read book Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations written by Victor A. Galaktionov and published by CRC Press. This book was released on 2014-09-22 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations. The authors present a unified approach to deal with these quasilinear PDEs.The book

Blow-up Theories for Semilinear Parabolic Equations

Author : Bei Hu
Publisher : Springer Science & Business Media
ISBN 13 : 3642184596
Total Pages : 137 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Blow-up Theories for Semilinear Parabolic Equations by : Bei Hu

Download or read book Blow-up Theories for Semilinear Parabolic Equations written by Bei Hu and published by Springer Science & Business Media. This book was released on 2011-03-23 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is an enormous amount of work in the literature about the blow-up behavior of evolution equations. It is our intention to introduce the theory by emphasizing the methods while seeking to avoid massive technical computations. To reach this goal, we use the simplest equation to illustrate the methods; these methods very often apply to more general equations.

Blow-up Theories for Semilinear Parabolic Equations

Author : Bei Hu
Publisher : Springer
ISBN 13 : 364218460X
Total Pages : 137 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Blow-up Theories for Semilinear Parabolic Equations by : Bei Hu

Download or read book Blow-up Theories for Semilinear Parabolic Equations written by Bei Hu and published by Springer. This book was released on 2011-03-17 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is an enormous amount of work in the literature about the blow-up behavior of evolution equations. It is our intention to introduce the theory by emphasizing the methods while seeking to avoid massive technical computations. To reach this goal, we use the simplest equation to illustrate the methods; these methods very often apply to more general equations.

Potential Estimates and Quasilinear Parabolic Equations with Measure Data

Author : Quoc-Hung Nguyen
Publisher : American Mathematical Society
ISBN 13 : 1470467224
Total Pages : 136 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Potential Estimates and Quasilinear Parabolic Equations with Measure Data by : Quoc-Hung Nguyen

Download or read book Potential Estimates and Quasilinear Parabolic Equations with Measure Data written by Quoc-Hung Nguyen and published by American Mathematical Society. This book was released on 2024-01-19 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Linear and Quasi-linear Equations of Parabolic Type

Author : Olʹga A. Ladyženskaja
Publisher : American Mathematical Soc.
ISBN 13 : 9780821815731
Total Pages : 74 pages
Book Rating : 4.8/5 (157 download)

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Book Synopsis Linear and Quasi-linear Equations of Parabolic Type by : Olʹga A. Ladyženskaja

Download or read book Linear and Quasi-linear Equations of Parabolic Type written by Olʹga A. Ladyženskaja and published by American Mathematical Soc.. This book was released on 1988 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt: Equations of parabolic type are encountered in many areas of mathematics and mathematical physics, and those encountered most frequently are linear and quasi-linear parabolic equations of the second order. In this volume, boundary value problems for such equations are studied from two points of view: solvability, unique or otherwise, and the effect of smoothness properties of the functions entering the initial and boundary conditions on the smoothness of the solutions.

Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications

Author : Victor A. Galaktionov
Publisher : CRC Press
ISBN 13 : 1135436266
Total Pages : 383 pages
Book Rating : 4.1/5 (354 download)

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Book Synopsis Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications by : Victor A. Galaktionov

Download or read book Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications written by Victor A. Galaktionov and published by CRC Press. This book was released on 2004-05-24 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike the classical Sturm theorems on the zeros of solutions of second-order ODEs, Sturm's evolution zero set analysis for parabolic PDEs did not attract much attention in the 19th century, and, in fact, it was lost or forgotten for almost a century. Briefly revived by Pólya in the 1930's and rediscovered in part several times since, it was not until the 1980's that the Sturmian argument for PDEs began to penetrate into the theory of parabolic equations and was found to have several fundamental applications. Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications focuses on geometric aspects of the intersection comparison for nonlinear models creating finite-time singularities. After introducing the original Sturm zero set results for linear parabolic equations and the basic concepts of geometric analysis, the author presents the main concepts and regularity results of the geometric intersection theory (G-theory). Here he considers the general singular equation and presents the geometric notions related to the regularity and interface propagation of solutions. In the general setting, the author describes the main aspects of the ODE-PDE duality, proves existence and nonexistence theorems, establishes uniqueness and optimal Bernstein-type estimates, and derives interface equations, including higher-order equations. The final two chapters explore some special aspects of discontinuous and continuous limit semigroups generated by singular parabolic equations. Much of the information presented here has never before been published in book form. Readable and self-contained, this book forms a unique and outstanding reference on second-order parabolic PDEs used as models for a wide range of physical problems.

Second Order Parabolic Differential Equations

Author : Gary M. Lieberman
Publisher : World Scientific
ISBN 13 : 9789810228835
Total Pages : 472 pages
Book Rating : 4.2/5 (288 download)

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Book Synopsis Second Order Parabolic Differential Equations by : Gary M. Lieberman

Download or read book Second Order Parabolic Differential Equations written by Gary M. Lieberman and published by World Scientific. This book was released on 1996 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction. Maximum principles. Introduction to the theory of weak solutions. Hölder estimates. Existence, uniqueness, and regularity of solutions. Further theory of weak solutions. Strong solutions. Fixed point theorems and their applications. Comparison and maximum principles. Boundary gradient estimates. Global and local gradient bounds. Hölder gradient estimates and existence theorems. The oblique derivative problem for quasilinear parabolic equations. Fully nonlinear equations. Introduction. Monge-Ampère and Hessian equations.

Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications

Author : Victor A. Galaktionov
Publisher : CRC Press
ISBN 13 : 0203998065
Total Pages : 384 pages
Book Rating : 4.2/5 (39 download)

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Book Synopsis Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications by : Victor A. Galaktionov

Partial Differential Equations of Parabolic Type

Author : Avner Friedman
Publisher : Courier Corporation
ISBN 13 : 0486318265
Total Pages : 369 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Partial Differential Equations of Parabolic Type by : Avner Friedman

Download or read book Partial Differential Equations of Parabolic Type written by Avner Friedman and published by Courier Corporation. This book was released on 2013-08-16 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this book, even readers unfamiliar with the field can acquire sufficient background to understand research literature related to the theory of parabolic and elliptic equations. 1964 edition.

Superlinear Parabolic Problems

Author : Pavol Quittner
Publisher : Springer Science & Business Media
ISBN 13 : 3764384425
Total Pages : 593 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Superlinear Parabolic Problems by : Pavol Quittner

Download or read book Superlinear Parabolic Problems written by Pavol Quittner and published by Springer Science & Business Media. This book was released on 2007-12-16 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology. The book is self-contained and up-to-date, taking special care on the didactical preparation of the material. It is devoted to problems that are intensively studied but have not been treated thus far in depth in the book literature.

Analytical and Numerical Methods for Convection-dominated and Singularly Perturbed Problems

Author : Lubin Vulkov
Publisher : Nova Publishers
ISBN 13 : 9781560728481
Total Pages : 298 pages
Book Rating : 4.7/5 (284 download)

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Book Synopsis Analytical and Numerical Methods for Convection-dominated and Singularly Perturbed Problems by : Lubin Vulkov

Download or read book Analytical and Numerical Methods for Convection-dominated and Singularly Perturbed Problems written by Lubin Vulkov and published by Nova Publishers. This book was released on 2000 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the Proceedings of the Workshop on Analytical and Computational Methods for Convection-Dominated and Singularly Perturbed Problems, which took place in Lozenetz, Bulgaria, 27-31 August 1998. The workshop attracted about 50 participants from 12 countries. The volume includes 13 invited lectures and 19 contributed papers presented at the workshop and thus gives an overview of the latest developments in both the theory and applications of advanced numerical methods to problems having boundary and interior layers. There was an emphasis on experiences from the numerical analysis of such problems and on theoretical developments. The aim of the workshop was to provide an opportunity for scientists from the East and the West, who develop robust methods for singularly perturbed and related problems and also who apply these methods to real-life problems, to discuss recent achievements in this area and to exchange ideas with a view of possible research co-operation.

Singular Solutions of Nonlinear Elliptic and Parabolic Equations

Author : Alexander A. Kovalevsky
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110332248
Total Pages : 447 pages
Book Rating : 4.1/5 (13 download)

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Book Synopsis Singular Solutions of Nonlinear Elliptic and Parabolic Equations by : Alexander A. Kovalevsky

Download or read book Singular Solutions of Nonlinear Elliptic and Parabolic Equations written by Alexander A. Kovalevsky and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-03-21 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph looks at several trends in the investigation of singular solutions of nonlinear elliptic and parabolic equations. It discusses results on the existence and properties of weak and entropy solutions for elliptic second-order equations and some classes of fourth-order equations with L1-data and questions on the removability of singularities of solutions to elliptic and parabolic second-order equations in divergence form. It looks at localized and nonlocalized singularly peaking boundary regimes for different classes of quasilinear parabolic second- and high-order equations in divergence form. The book will be useful for researchers and post-graduate students that specialize in the field of the theory of partial differential equations and nonlinear analysis. Contents: Foreword Part I: Nonlinear elliptic equations with L^1-data Nonlinear elliptic equations of the second order with L^1-data Nonlinear equations of the fourth order with strengthened coercivity and L^1-data Part II: Removability of singularities of the solutions of quasilinear elliptic and parabolic equations of the second order Removability of singularities of the solutions of quasilinear elliptic equations Removability of singularities of the solutions of quasilinear parabolic equations Quasilinear elliptic equations with coefficients from the Kato class Part III: Boundary regimes with peaking for quasilinear parabolic equations Energy methods for the investigation of localized regimes with peaking for parabolic second-order equations Method of functional inequalities in peaking regimes for parabolic equations of higher orders Nonlocalized regimes with singular peaking Appendix: Formulations and proofs of the auxiliary results Bibliography

Blow-Up in Nonlinear Equations of Mathematical Physics

Author : Maxim Olegovich Korpusov
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110602075
Total Pages : 344 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Blow-Up in Nonlinear Equations of Mathematical Physics by : Maxim Olegovich Korpusov

Download or read book Blow-Up in Nonlinear Equations of Mathematical Physics written by Maxim Olegovich Korpusov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-08-06 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book carefully studies the blow-up phenomenon of solutions to partial differential equations, including many equations of mathematical physics. The included material is based on lectures read by the authors at the Lomonosov Moscow State University, and the book is addressed to a wide range of researchers and graduate students working in nonlinear partial differential equations, nonlinear functional analysis, and mathematical physics. Contents Nonlinear capacity method of S. I. Pokhozhaev Method of self-similar solutions of V. A. Galaktionov Method of test functions in combination with method of nonlinear capacity Energy method of H. A. Levine Energy method of G. Todorova Energy method of S. I. Pokhozhaev Energy method of V. K. Kalantarov and O. A. Ladyzhenskaya Energy method of M. O. Korpusov and A. G. Sveshnikov Nonlinear Schrödinger equation Variational method of L. E. Payne and D. H. Sattinger Breaking of solutions of wave equations Auxiliary and additional results

Blow-up in Nonlinear Sobolev Type Equations

Author : A. B. Alʹshin
Publisher : Walter de Gruyter
ISBN 13 : 3110255278
Total Pages : 661 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Blow-up in Nonlinear Sobolev Type Equations by : A. B. Alʹshin

Download or read book Blow-up in Nonlinear Sobolev Type Equations written by A. B. Alʹshin and published by Walter de Gruyter. This book was released on 2011 with total page 661 pages. Available in PDF, EPUB and Kindle. Book excerpt: The monograph is devoted to the study of initial-boundary-value problems for multi-dimensional Sobolev-type equations over bounded domains. The authors consider both specific initial-boundary-value problems and abstract Cauchy problems for first-order (in the time variable) differential equations with nonlinear operator coefficients with respect to spatial variables. The main aim of the monograph is to obtain sufficient conditions for global (in time) solvability, to obtain sufficient conditions for blow-up of solutions at finite time, and to derive upper and lower estimates for the blow-up time. The abstract results apply to a large variety of problems. Thus, the well-known Benjamin-Bona-Mahony-Burgers equation and Rosenau-Burgers equations with sources and many other physical problems are considered as examples. Moreover, the method proposed for studying blow-up phenomena for nonlinear Sobolev-type equations is applied to equations which play an important role in physics. For instance, several examples describe different electrical breakdown mechanisms in crystal semiconductors, as well as the breakdown in the presence of sources of free charges in a self-consistent electric field. The monograph contains a vast list of references (440 items) and gives an overall view of the contemporary state-of-the-art of the mathematical modeling of various important problems arising in physics. Since the list of references contains many papers which have been published previously only in Russian research journals, it may also serve as a guide to the Russian literature.

Differential Equations and Dynamical Systems

Author : Abdulla Azamov
Publisher : Springer
ISBN 13 : 3030014762
Total Pages : 195 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Differential Equations and Dynamical Systems by : Abdulla Azamov

Download or read book Differential Equations and Dynamical Systems written by Abdulla Azamov and published by Springer. This book was released on 2018-10-20 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features papers presented during a special session on dynamical systems, mathematical physics, and partial differential equations. Research articles are devoted to broad complex systems and models such as qualitative theory of dynamical systems, theory of games, circle diffeomorphisms, piecewise smooth circle maps, nonlinear parabolic systems, quadtratic dynamical systems, billiards, and intermittent maps. Focusing on a variety of topics from dynamical properties to stochastic properties of dynamical systems, this volume includes discussion on discrete-numerical tracking, conjugation between two critical circle maps, invariance principles, and the central limit theorem. Applications to game theory and networks are also included. Graduate students and researchers interested in complex systems, differential equations, dynamical systems, functional analysis, and mathematical physics will find this book useful for their studies. The special session was part of the second USA-Uzbekistan Conference on Analysis and Mathematical Physics held on August 8-12, 2017 at Urgench State University (Uzbekistan). The conference encouraged communication and future collaboration among U.S. mathematicians and their counterparts in Uzbekistan and other countries. Main themes included algebra and functional analysis, dynamical systems, mathematical physics and partial differential equations, probability theory and mathematical statistics, and pluripotential theory. A number of significant, recently established results were disseminated at the conference’s scheduled plenary talks, while invited talks presented a broad spectrum of findings in several sessions. Based on a different session from the conference, Algebra, Complex Analysis, and Pluripotential Theory is also published in the Springer Proceedings in Mathematics & Statistics Series.