Dedicated to him, Nonlinear Evolution Equations and Related Topics contains research papers written by highly distinguished mathematicians.

Author: Wolfgang Arendt

Publisher: Birkhäuser

ISBN: 9783034879248

Category: Mathematics

Page: 807

View: 304

Philippe Bénilan was a most original and charismatic mathematician who had a deep and decisive impact on the theory of Nonlinear Evolution Equations. Dedicated to him, Nonlinear Evolution Equations and Related Topics contains research papers written by highly distinguished mathematicians. They are all related to Philippe Benilan's work and reflect the present state of this most active field. The contributions cover a wide range of nonlinear and linear equations.

M.B. Benboubker, S. Ouaro, U. Traoré; Entropy solutions for nonhomogeneous Neumann problems involving the generalized p(x)-Laplacian operators and measure data, Journal of Nonlinear Evolution Equation and Application.

Author: Alexander L. SakhnovichPublish On: 2013-07-31

J. Funct. Anal., 144:359–370, 1997. A. L. Sakhnovich. Inverse spectral problem related to the N-wave equation. In: V. M. Adamyan et al. (eds). Differential operators and related topics. I, pp. 323–338. Oper. Theory Adv. Appl. 117.

Author: Alexander L. Sakhnovich

Publisher: Walter de Gruyter

ISBN: 9783110258615

Category: Mathematics

Page: 354

View: 440

This book is based on the method of operator identities and related theory of S-nodes, both developed by Lev Sakhnovich. The notion of the transfer matrix function generated by the S-node plays an essential role. The authors present fundamental solutions of various important systems of differential equations using the transfer matrix function, that is, either directly in the form of the transfer matrix function or via the representation in this form of the corresponding Darboux matrix, when Bäcklund–Darboux transformations and explicit solutions are considered. The transfer matrix function representation of the fundamental solution yields solution of an inverse problem, namely, the problem to recover system from its Weyl function. Weyl theories of selfadjoint and skew-selfadjoint Dirac systems, related canonical systems, discrete Dirac systems, system auxiliary to the N-wave equation and a system rationally depending on the spectral parameter are obtained in this way. The results on direct and inverse problems are applied in turn to the study of the initial-boundary value problems for integrable (nonlinear) wave equations via inverse spectral transformation method. Evolution of the Weyl function and solution of the initial-boundary value problem in a semi-strip are derived for many important nonlinear equations. Some uniqueness and global existence results are also proved in detail using evolution formulas. The reading of the book requires only some basic knowledge of linear algebra, calculus and operator theory from the standard university courses.

... the proof of Theorem 1.1 under the assumption of classic solvability of regularized problems associated with (1.2). ... initial boundary value problem for general fully nonlinear evolution equations is the subject of the book [10, ...

Author: Alexander I. Nazarov

Publisher: American Mathematical Soc.

ISBN: 9780821849972

Category: Mathematics

Page: 252

View: 166

This book contains papers that engage a wide set of classical and modern topics in partial differential equations, including linear and nonlinear equations, variational problems, the Navier-Stokes system, and the Boltzmann equation. The results include existence and uniqueness theorems, qualitative properties of solutions, a priori estimates, and nonexistence theorems. Table of Contents: J. Andersson, H. Shahgholian, and G. S. Weiss -- Regularity below the $C^2$ threshold for a torsion problem, based on regularity for Hamilton-Jacobi equations; A. Arkhipova -- Signorini-type problem in $\mathbb{R}^N$ for a class of quadratic functional; M. Bildhauer and M. Fuchs -- A 2D-invariant of a theorem of Uraltseva and Urdaletova for higher order variational problems; M. Bostan, I. M. Gamba, and T. Goudon -- The linear Boltzmann equation with space periodic electric field; L. Caffarelli and L. Silvestre -- Smooth approximations of solutions to nonconvex fully nonlinear elliptic equations; P. Constantin and G. Seregin -- Holder continuity of solutions of 2D Navier-Stokes equations with singular forcing; M. Giaquinta, P. M. Mariano, G. Modica, and D. Mucci -- Currents and curvature varifolds in continuum mechanics; N. M. Ivochkina -- On classic solvability of the $m$-Hessian evolution equation; N. V. Krylov -- About an example of N. N. Ural'tseva and weak uniqueness for elliptic operators; V. Maz'ya and R. McOwen -- On the fundamental solution of an elliptic equation in nondivergence form; G. Mingione -- Boundary regularity for vectorial problems; A. Nazarov and A. Reznikov -- Attainability of infima in the critical Sobolev trace embedding theorem on manifolds; M. V. Safonov -- Non-divergence elliptic equations of second order with unbounded drift; V. V. Zhikov and S. E. Pastukhova -- Global solvability of Navier-Stokes equations for a nonhomogeneous non-Newtonian fluid. (TRANS2/229)

This model suggests a relevant generalized context in which all the questions we have already posed may again be asked. ... of the Tulane Program in Partial Differential Equations and Related Topics, Lecture Notes in Mathematics, No.

Author: Michael G. Crandall

Publisher: Elsevier

ISBN: 9781483269283

Category: Mathematics

Page: 266

View: 168

Nonlinear Evolution Equation covers the proceedings of the Symposium by the same title, conducted by the Mathematics Research Center at the University of Wisconsin, Madison on October 17-19, 1977. This book is divided into 13 chapters and begins with reviews of the uniqueness of solution to systems of conservation laws and the computational aspects of Glimm’s method. The next chapters examine the theoretical and practical aspects of Boltzmann, Navier-Stokes, and evolution equations. These topics are followed by discussions of the practical applications of Trotter’s product formula for some nonlinear semigroups and the finite time blow-up in nonlinear problems. The closing chapters deal with a Hamiltonian approach to the K-dV and other equations, along with a variational method for finding periodic solutions of differential equations. This book will prove useful to mathematicians and engineers.

The Emphasis Year 2002-2003 Program on Nonlinear Partial Differential Equations and Related Analysis, ... Abstract evolution equations, linear and quasilinear, revisited, in, Functional Analgsis and Related Topics (H. Komatsu, ed.) ...

Author: Gui-Qiang Chen

Publisher: American Mathematical Soc.

ISBN: 9780821835333

Category: Mathematics

Page: 323

View: 347

The Emphasis Year on Nonlinear Partial Differential Equations and Related Analysis at Northwestern University produced this fine collection of original research and survey articles. Many well-known mathematicians attended the events and submitted their contributions for this volume. Eighteen papers comprise this work, representing the most significant advances and current trends in nonlinear PDEs and their applications. Topics covered include elliptic and parabolic equations, Navier Stokes equations, and hyperbolic conservation laws. Important applications are presented from incompressible and compressible fluid mechanics, combustion, and electromagnetism.Also included are articles on recent advances in statistical reliability in modeling, simulation, level set methods for image processing, shock waves, free boundaries, boundary layers, errors in numerical solutions, stability, instability, and singular limits. The volume is suitable for researchers and graduate students interested in partial differential equations.

Contents Part I Integrable Systems in (2+1)-Dimensions Solitons and Dromions, Coherent Structures in a Nonlinear World By P.M. Santini and A.S. Fokas (With 2 Figures) . . . . . . . . . . . . . . . . Boundary Value Problems in 1+1 and in ...

Author: Sandra Carillo

Publisher: Springer Science & Business Media

ISBN: 9783642840395

Category: Science

Page: 233

View: 240

Nonlinear Evolution Equations and Dynamical Systems (NEEDS) provides a presentation of the state of the art. Except for a few review papers, the 40 contributions are intentially brief to give only the gist of the methods, proofs, etc. including references to the relevant litera- ture. This gives a handy overview of current research activities. Hence, the book should be equally useful to the senior resercher as well as the colleague just entering the field. Keypoints treated are: i) integrable systems in multidimensions and associated phenomenology ("dromions"); ii) criteria and tests of integrability (e.g., Painlev test); iii) new developments related to the scattering transform; iv) algebraic approaches to integrable systems and Hamiltonian theory (e.g., connections with Young-Baxter equations and Kac-Moody algebras); v) new developments in mappings and cellular automata, vi) applications to general relativity, condensed matter physics, and oceanography.

[126] T. Nishida, Nonlinear Hyperbolic Equations and Related Topics in Fluid Dynamics. Publ. Math. d'Orsay, 78.02, Paris, 1978. [127] K. Nishihara, Convergence Rates to Nonlinear Diffusion Waves for Solutions of System ...

Author: Pascal Cherrier

Publisher: American Mathematical Soc.

ISBN: 9780821875766

Category: Mathematics

Page: 377

View: 424

This book considers evolution equations of hyperbolic and parabolic type. These equations are studied from a common point of view, using elementary methods, such as that of energy estimates, which prove to be quite versatile. The authors emphasize the Cauchy problem and present a unified theory for the treatment of these equations. In particular, they provide local and global existence results, as well as strong well-posedness and asymptotic behavior results for the Cauchy problem for quasi-linear equations. Solutions of linear equations are constructed explicitly, using the Galerkin method; the linear theory is then applied to quasi-linear equations, by means of a linearization and fixed-point technique. The authors also compare hyperbolic and parabolic problems, both in terms of singular perturbations, on compact time intervals, and asymptotically, in terms of the diffusion phenomenon, with new results on decay estimates for strong solutions of homogeneous quasi-linear equations of each type. This textbook presents a valuable introduction to topics in the theory of evolution equations, suitable for advanced graduate students. The exposition is largely self-contained. The initial chapter reviews the essential material from functional analysis. New ideas are introduced along with their context. Proofs are detailed and carefully presented. The book concludes with a chapter on applications of the theory to Maxwell's equations and von Karman's equations.

This book will provide the background of fundamental ideas and classical Lagrangian approach to understand nonlinear real-world wave phenomena, soliton dynamics, symmetry, supersymmetric realization and some important methods for solving ...

Author: Amitava Choudhuri

Publisher: LAP Lambert Academic Publishing

ISBN: 3845441801

Category:

Page: 132

View: 698

The active area of research investigation during the past sixty years has been the study of solitons and related nonlinear real world phenomena that cannot be explained with the linear evolution equations. A Lagrangian based approach has been derived to study the properties of the nonlinear evolution equations. This book will provide the background of fundamental ideas and classical Lagrangian approach to understand nonlinear real-world wave phenomena, soliton dynamics, symmetry, supersymmetric realization and some important methods for solving the nonlinear equations up to the level of present-day active research on these and related topics. I hope this will stimulate future research on understanding the nonlinear problems and may be a useful source book for researchers, graduate students enrolled in M.S and Ph.D degree programs. Considering the multidisciplinary nature and important applications almost all universities offer a high-level graduate course devoted to frontier topics like nonlinear wave theory, integrable systems, solitons, symmetry and supersymmetry. It will be a useful text for graduate and senior-level courses dealing with above topics.

In these lectures, we discuss three closely related topics. We first discuss derivation of the nonlinear evolution equation for surface acoustic waves and show that all known methods of derivation should and do give the same evolution ...

Author: M. Destrade

Publisher: Springer Science & Business Media

ISBN: 9783211735725

Category: Technology & Engineering

Page: 281

View: 685

Papers in this book provide a state-of-the-art examination of waves in pre-stressed materials. You’ll gain new perspectives via a multi-disciplinary approach that interweaves key topics. These topics include the mathematical modeling of incremental material response (elastic and inelastic), an analysis of the governing differential equations, and boundary-value problems. Detailed illustrations help you visualize key concepts and processes.