Author: Herbert GajewskiPublisher:
ISBN:
Category :
Languages : en
Pages : 9
Book Description
About Loss of Regularity and "blow Up" of Solutions for Quasilinear Parabolic Systems
Author: Herbert GajewskiAbout loss of regularity and "blow up" of solutions for quasilinear parabolic systems
Author: Herbert GajewskiBlow-Up in Quasilinear Parabolic Equations
Author: A. A. SamarskiiPublisher: Walter de Gruyter
ISBN: 3110889862
Category : Mathematics
Languages : en
Pages : 561
Book Description
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)
Regularity Problem for Quasilinear Elliptic and Parabolic Systems
Author: Alexander KoshelevPublisher: Springer
ISBN: 3540447725
Category : Mathematics
Languages : en
Pages : 277
Book Description
The smoothness of solutions for quasilinear systems is one of the most important problems in modern mathematical physics. This book deals with regular or strong solutions for general quasilinear second-order elliptic and parabolic systems. Applications in solid mechanics, hydrodynamics, elasticity and plasticity are described. The results presented are based on two main ideas: the universal iterative method, and explicit, sometimes sharp, coercivity estimates in weighted spaces. Readers are assumed to have a standard background in analysis and PDEs.
Regularity of solutions for some quasilinear parabolic systems
Author: Aleksandr KošelevSuperlinear Parabolic Problems
Author: Pavol QuittnerPublisher: Springer Science & Business Media
ISBN: 3764384425
Category : Mathematics
Languages : en
Pages : 593
Book Description
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.
Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations
Author: Victor A. GalaktionovPublisher: CRC Press
ISBN: 1482251736
Category : Mathematics
Languages : en
Pages : 565
Book Description
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
Regularity of Solutions for Some Quasilinear Parabolic Systems
Author: A. KoshelevLinear and Quasilinear Parabolic Systems: Sobolev Space Theory
Author: David HoffPublisher: American Mathematical Soc.
ISBN: 1470461617
Category : Education
Languages : en
Pages : 226
Book Description
This monograph presents a systematic theory of weak solutions in Hilbert-Sobolev spaces of initial-boundary value problems for parabolic systems of partial differential equations with general essential and natural boundary conditions and minimal hypotheses on coefficients. Applications to quasilinear systems are given, including local existence for large data, global existence near an attractor, the Leray and Hopf theorems for the Navier-Stokes equations and results concerning invariant regions. Supplementary material is provided, including a self-contained treatment of the calculus of Sobolev functions on the boundaries of Lipschitz domains and a thorough discussion of measurability considerations for elements of Bochner-Sobolev spaces. This book will be particularly useful both for researchers requiring accessible and broadly applicable formulations of standard results as well as for students preparing for research in applied analysis. Readers should be familiar with the basic facts of measure theory and functional analysis, including weak derivatives and Sobolev spaces. Prior work in partial differential equations is helpful but not required.
Blow-up Theories for Semilinear Parabolic Equations
Author: Bei HuPublisher: Springer Science & Business Media
ISBN: 3642184596
Category : Mathematics
Languages : en
Pages : 137
Book Description
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.