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Well Posedness Of Parabolic Difference Equations
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Book Synopsis Well-Posedness of Parabolic Difference Equations by : A. Ashyralyev
Download or read book Well-Posedness of Parabolic Difference Equations written by A. Ashyralyev and published by Birkhäuser. This book was released on 2012-12-06 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: A well-known and widely applied method of approximating the solutions of problems in mathematical physics is the method of difference schemes. Modern computers allow the implementation of highly accurate ones; hence, their construction and investigation for various boundary value problems in mathematical physics is generating much current interest. The present monograph is devoted to the construction of highly accurate difference schemes for parabolic boundary value problems, based on Padé approximations. The investigation is based on a new notion of positivity of difference operators in Banach spaces, which allows one to deal with difference schemes of arbitrary order of accuracy. Establishing coercivity inequalities allows one to obtain sharp, that is, two-sided estimates of convergence rates. The proofs are based on results in interpolation theory of linear operators. This monograph will be of value to professional mathematicians as well as advanced students interested in the fields of functional analysis and partial differential equations.
Book Synopsis Well-posedness of Parabolic Difference Equations by : Allaberen Ashyralyev
Download or read book Well-posedness of Parabolic Difference Equations written by Allaberen Ashyralyev and published by Birkhauser. This book was released on 1994 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: A well-known and widely applied method of approximating the solutions of problems in mathematical physics is the method of difference schemes. Modern computers allow the implementation of highly accurate ones; hence, their construction and investigation for various boundary value problems in mathematical physics is generating much current interest. The present monograph is devoted to the construction of highly accurate difference schemes for parabolic boundary value problems, based on PadA(c) approximations. The investigation is based on a new notion of positivity of difference operators in Banach spaces, which allows one to deal with difference schemes of arbitrary order of accuracy. Establishing coercivity inequalities allows one to obtain sharp, that is, two-sided estimates of convergence rates. The proofs are based on results in interpolation theory of linear operators. This monograph will be of value to professional mathematicians as well as advanced students interested in the fields of functional analysis and partial differential equations.
Book Synopsis Parabolic Equations with Irregular Data and Related Issues by : Claude Le Bris
Download or read book Parabolic Equations with Irregular Data and Related Issues written by Claude Le Bris and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-06-17 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the existence and uniqueness of solutions to parabolic-type equations with irregular coefficients and/or initial conditions. It elaborates on the DiPerna-Lions theory of renormalized solutions to linear transport equations and related equations, and also examines the connection between the results on the partial differential equation and the well-posedness of the underlying stochastic/ordinary differential equation.
Book Synopsis Global Well-posedness of Nonlinear Parabolic-Hyperbolic Coupled Systems by : Yuming Qin
Download or read book Global Well-posedness of Nonlinear Parabolic-Hyperbolic Coupled Systems written by Yuming Qin and published by Springer Science & Business Media. This book was released on 2012-02-28 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent results on nonlinear parabolic-hyperbolic coupled systems such as the compressible Navier-Stokes equations, and liquid crystal system. It summarizes recently published research by the authors and their collaborators, but also includes new and unpublished material. All models under consideration are built on compressible equations and liquid crystal systems. This type of partial differential equations arises not only in many fields of mathematics, but also in other branches of science such as physics, fluid dynamics and material science.
Book Synopsis New Difference Schemes for Partial Differential Equations by : Allaberen Ashyralyev
Download or read book New Difference Schemes for Partial Differential Equations written by Allaberen Ashyralyev and published by Birkhäuser. This book was released on 2012-12-06 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores new difference schemes for approximating the solutions of regular and singular perturbation boundary-value problems for PDEs. The construction is based on the exact difference scheme and Taylor's decomposition on the two or three points, which permits investigation of differential equations with variable coefficients and regular and singular perturbation boundary value problems.
Book Synopsis General Parabolic Mixed Order Systems in Lp and Applications by : Robert Denk
Download or read book General Parabolic Mixed Order Systems in Lp and Applications written by Robert Denk and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text, a theory for general linear parabolic partial differential equations is established which covers equations with inhomogeneous symbol structure as well as mixed-order systems. Typical applications include several variants of the Stokes system and free boundary value problems. We show well-posedness in Lp-Lq-Sobolev spaces in time and space for the linear problems (i.e., maximal regularity) which is the key step for the treatment of nonlinear problems. The theory is based on the concept of the Newton polygon and can cover equations which are not accessible by standard methods as, e.g., semigroup theory. Results are obtained in different types of non-integer Lp-Sobolev spaces as Besov spaces, Bessel potential spaces, and Triebel–Lizorkin spaces. The last-mentioned class appears in a natural way as traces of Lp-Lq-Sobolev spaces. We also present a selection of applications in the whole space and on half-spaces. Among others, we prove well-posedness of the linearizations of the generalized thermoelastic plate equation, the two-phase Navier–Stokes equations with Boussinesq–Scriven surface, and the Lp-Lq two-phase Stefan problem with Gibbs–Thomson correction.
Book Synopsis Fractional Quantum Mechanics by : Laskin Nick
Download or read book Fractional Quantum Mechanics written by Laskin Nick and published by World Scientific. This book was released on 2018-05-25 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional quantum mechanics is a recently emerged and rapidly developing field of quantum physics. This is the first monograph on fundamentals and physical applications of fractional quantum mechanics, written by its founder. The fractional Schrödinger equation and the fractional path integral are new fundamental physical concepts introduced and elaborated in the book. The fractional Schrödinger equation is a manifestation of fractional quantum mechanics. The fractional path integral is a new mathematical tool based on integration over Lévy flights. The fractional path integral method enhances the well-known Feynman path integral framework. Related topics covered in the text include time fractional quantum mechanics, fractional statistical mechanics, fractional classical mechanics and the α-stable Lévy random process. The book is well-suited for theorists, pure and applied mathematicians, solid-state physicists, chemists, and others working with the Schrödinger equation, the path integral technique and applications of fractional calculus in various research areas. It is useful to skilled researchers as well as to graduate students looking for new ideas and advanced approaches.
Book Synopsis Linear Discrete Parabolic Problems by : Nikolai Bakaev
Download or read book Linear Discrete Parabolic Problems written by Nikolai Bakaev and published by Elsevier. This book was released on 2005-12-02 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume introduces a unified, self-contained study of linear discrete parabolic problems through reducing the starting discrete problem to the Cauchy problem for an evolution equation in discrete time. Accessible to beginning graduate students, the book contains a general stability theory of discrete evolution equations in Banach space and gives applications of this theory to the analysis of various classes of modern discretization methods, among others, Runge-Kutta and linear multistep methods as well as operator splitting methods. Key features: * Presents a unified approach to examining discretization methods for parabolic equations. * Highlights a stability theory of discrete evolution equations (discrete semigroups) in Banach space. * Deals with both autonomous and non-autonomous equations as well as with equations with memory. * Offers a series of numerous well-posedness and convergence results for various discretization methods as applied to abstract parabolic equations; among others, Runge-Kutta and linear multistep methods as well as certain operator splitting methods. * Provides comments of results and historical remarks after each chapter. · Presents a unified approach to examining discretization methods for parabolic equations. · Highlights a stability theory of discrete evolution equations (discrete semigroups) in Banach space. · Deals with both autonomous and non-autonomous equations as well as with equations with memory. · Offers a series of numerous well-posedness and convergence results for various discretization methods as applied to abstract parabolic equations; among others, Runge-Kutta and linear multistep methods as well as certain operator splitting methods as well as certain operator splitting methods are studied in detail. ·Provides comments of results and historical remarks after each chapter.
Book Synopsis Partial Differential Equations and the Finite Element Method by : Pavel Ŝolín
Download or read book Partial Differential Equations and the Finite Element Method written by Pavel Ŝolín and published by John Wiley & Sons. This book was released on 2005-12-16 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic introduction to partial differential equations and modern finite element methods for their efficient numerical solution Partial Differential Equations and the Finite Element Method provides a much-needed, clear, and systematic introduction to modern theory of partial differential equations (PDEs) and finite element methods (FEM). Both nodal and hierachic concepts of the FEM are examined. Reflecting the growing complexity and multiscale nature of current engineering and scientific problems, the author emphasizes higher-order finite element methods such as the spectral or hp-FEM. A solid introduction to the theory of PDEs and FEM contained in Chapters 1-4 serves as the core and foundation of the publication. Chapter 5 is devoted to modern higher-order methods for the numerical solution of ordinary differential equations (ODEs) that arise in the semidiscretization of time-dependent PDEs by the Method of Lines (MOL). Chapter 6 discusses fourth-order PDEs rooted in the bending of elastic beams and plates and approximates their solution by means of higher-order Hermite and Argyris elements. Finally, Chapter 7 introduces the reader to various PDEs governing computational electromagnetics and describes their finite element approximation, including modern higher-order edge elements for Maxwell's equations. The understanding of many theoretical and practical aspects of both PDEs and FEM requires a solid knowledge of linear algebra and elementary functional analysis, such as functions and linear operators in the Lebesgue, Hilbert, and Sobolev spaces. These topics are discussed with the help of many illustrative examples in Appendix A, which is provided as a service for those readers who need to gain the necessary background or require a refresher tutorial. Appendix B presents several finite element computations rooted in practical engineering problems and demonstrates the benefits of using higher-order FEM. Numerous finite element algorithms are written out in detail alongside implementation discussions. Exercises, including many that involve programming the FEM, are designed to assist the reader in solving typical problems in engineering and science. Specifically designed as a coursebook, this student-tested publication is geared to upper-level undergraduates and graduate students in all disciplines of computational engineeringand science. It is also a practical problem-solving reference for researchers, engineers, and physicists.
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.
Book Synopsis Parabolic Equations on an Infinite Strip by : Watson
Download or read book Parabolic Equations on an Infinite Strip written by Watson and published by Routledge. This book was released on 2017-10-02 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on solutions of second order, linear, parabolic, partial differentialequations on an infinite strip-emphasizing their integral representation, their initialvalues in several senses, and the relations between these.Parabolic Equations on an Infinite Strip provides valuable information-previously unavailable in a single volume-on such topics as semigroup property.. . the Cauchy problem ... Gauss-Weierstrass representation . .. initial limits .. .normal limits and related representation theorems ... hyperplane conditions .. .determination of the initial measure .. . and the maximum principle. It also exploresnew, unpublished results on parabolic limits . . . more general limits ... and solutionssatisfying LP conditions.Requiring only a fundamental knowledge of general analysis and measure theory, thisbook serves as an excellent text for graduate students studying partial differentialequations and harmonic analysis, as well as a useful reference for analysts interested inapplied measure theory, and specialists in partial differential equations.
Book Synopsis Proceedings of the Conference on Differential & Difference Equations and Applications by : Ravi P. Agarwal
Download or read book Proceedings of the Conference on Differential & Difference Equations and Applications written by Ravi P. Agarwal and published by Hindawi Publishing Corporation. This book was released on 2006 with total page 1268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 . This book was released on 1964 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Attractors for Degenerate Parabolic Type Equations by : Messoud Efendiev
Download or read book Attractors for Degenerate Parabolic Type Equations written by Messoud Efendiev and published by American Mathematical Soc.. This book was released on 2013-09-26 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the long-time behavior of solutions of degenerate parabolic dissipative equations arising in the study of biological, ecological, and physical problems. Examples include porous media equations, -Laplacian and doubly nonlinear equations, as well as degenerate diffusion equations with chemotaxis and ODE-PDE coupling systems. For the first time, the long-time dynamics of various classes of degenerate parabolic equations, both semilinear and quasilinear, are systematically studied in terms of their global and exponential attractors. The long-time behavior of many dissipative systems generated by evolution equations of mathematical physics can be described in terms of global attractors. In the case of dissipative PDEs in bounded domains, this attractor usually has finite Hausdorff and fractal dimension. Hence, if the global attractor exists, its defining property guarantees that the dynamical system reduced to the attractor contains all of the nontrivial dynamics of the original system. Moreover, the reduced phase space is really "thinner" than the initial phase space. However, in contrast to nondegenerate parabolic type equations, for a quite large class of degenerate parabolic type equations, their global attractors can have infinite fractal dimension. The main goal of the present book is to give a detailed and systematic study of the well-posedness and the dynamics of the semigroup associated to important degenerate parabolic equations in terms of their global and exponential attractors. Fundamental topics include existence of attractors, convergence of the dynamics and the rate of convergence, as well as the determination of the fractal dimension and the Kolmogorov entropy of corresponding attractors. The analysis and results in this book show that there are new effects related to the attractor of such degenerate equations that cannot be observed in the case of nondegenerate equations in bounded domains. This book is published in cooperation with Real Sociedad Matemática Española (RSME).
Book Synopsis Improperly Posed Problems in Partial Differential Equations by : L. E. Payne
Download or read book Improperly Posed Problems in Partial Differential Equations written by L. E. Payne and published by SIAM. This book was released on 1975-06-01 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: A discussion of improperly posed Cauchy problems in partial differential equations
Download or read book Further Progress in Analysis written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :International Society for Analysis, Applications, and Computation. Congress Publisher :World Scientific ISBN 13 :9812837329 Total Pages :877 pages Book Rating :4.8/5 (128 download)
Book Synopsis Further Progress in Analysis by : International Society for Analysis, Applications, and Computation. Congress
Download or read book Further Progress in Analysis written by International Society for Analysis, Applications, and Computation. Congress and published by World Scientific. This book was released on 2009 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ISAAC (International Society for Analysis, its Applications and Computation) Congress, which has been held every second year since 1997, covers the major progress in analysis, applications and computation in recent years. In this proceedings volume, plenary lectures highlight the recent research results, while 17 sessions organized by well-known specialists reflect the state of the art of important subfields. This volume concentrates on partial differential equations, function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, inverse problems, functional differential and difference equations and integrable systems.
