Superlinear Parabolic Problems
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Superlinear Parabolic Problems
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Author : Prof. Dr. Pavol Quittner
language : en
Publisher: Springer
Release Date : 2019-06-13
Superlinear Parabolic Problems written by Prof. Dr. Pavol Quittner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-13 with Mathematics categories.
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 first two chapters introduce to the field and enable the reader to get acquainted with the main ideas by studying simple model problems, respectively of elliptic and parabolic type. The subsequent three chapters are devoted to problems with more complex structure; namely, elliptic and parabolic systems, equations with gradient depending nonlinearities, and nonlocal equations. They include many developments which reflect several aspects of current research. Although the techniques introduced in the first two chapters provide efficient tools to attack some aspects of these problems, they often display new phenomena and specifically different behaviors, whose study requires new ideas. Many open problems are mentioned and commented. The book is self-contained and up-to-date, it has a high didactic quality. It is devoted to problems that are intensively studied but have not been treated so far in depth in the book literature. The intended audience includes graduate and postgraduate students and researchers working in the field of partial differential equations and applied mathematics. The first edition of this book has become one of the standard references in the field. This second edition provides a revised text and contains a number of updates reflecting significant recent advances that have appeared in this growing field since the first edition.
Superlinear Parabolic Problems
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Author : Pavol Quittner
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-16
Superlinear Parabolic Problems written by Pavol Quittner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-16 with Mathematics categories.
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.
Linear And Quasilinear Parabolic Problems
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Author : Herbert Amann
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-03-27
Linear And Quasilinear Parabolic Problems written by Herbert Amann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-03-27 with Language Arts & Disciplines categories.
This treatise gives an exposition of the functional analytical approach to quasilinear parabolic evolution equations, developed to a large extent by the author during the last 10 years. This approach is based on the theory of linear nonautonomous parabolic evolution equations and on interpolation-extrapolation techniques. It is the only general method that applies to noncoercive quasilinear parabolic systems under nonlinear boundary conditions. The present first volume is devoted to a detailed study of nonautonomous linear parabolic evolution equations in general Banach spaces. It contains a careful exposition of the constant domain case, leading to some improvements of the classical Sobolevskii-Tanabe results. It also includes recent results for equations possessing constant interpolation spaces. In addition, systematic presentations of the theory of maximal regularity in spaces of continuous and Hölder continuous functions, and in Lebesgue spaces, are given. It includes related recent theorems in the field of harmonic analysis in Banach spaces and on operators possessing bounded imaginary powers. Lastly, there is a complete presentation of the technique of interpolation-extrapolation spaces and of evolution equations in those spaces, containing many new results.
Linear Discrete Parabolic Problems
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Author : Nikolai Bakaev
language : en
Publisher: Elsevier
Release Date : 2005-12-02
Linear Discrete Parabolic Problems written by Nikolai Bakaev and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-02 with Mathematics categories.
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.
Nonlinear Elliptic And Parabolic Problems
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Author : Michel Chipot
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-09
Nonlinear Elliptic And Parabolic Problems written by Michel Chipot and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-09 with Mathematics categories.
Celebrates the work of the renowned mathematician Herbert Amann, who had a significant and decisive influence in shaping Nonlinear Analysis. Containing 32 contributions, this volume covers a range of nonlinear elliptic and parabolic equations, with applications to natural sciences and engineering.
Elliptic And Parabolic Problems
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Author : Josef Bemelmans
language : en
Publisher: World Scientific
Release Date : 2002-08-06
Elliptic And Parabolic Problems written by Josef Bemelmans and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-06 with Mathematics categories.
This book provides an overview of the state of the art in important subjects, including — besides elliptic and parabolic issues — geometry, free boundary problems, fluid mechanics, evolution problems in general, calculus of variations, homogenization, control, modeling and numerical analysis. Contents:Rolduc:Models for Shape Memory Alloys Described by Subdifferentials of Indicator Functions (T Aiki & N Kenmochi)Local Stability Under Changes of Boundary Conditions at a Far Away Location (M Chipot & A Rougirel)Existence of Solutions of a Segregation Model Arising in Population Dynamics (G Galiano et al.)Global Attractors for Multivalued Flows Associated with Subdifferentials (N Kenmochi & N Yamazaki)Quasiconvexity and Optimal Design (P Pedregal)A Comparison Principle for the p-Laplacian (A Poliakovsky & I Shafrir)Gaeta:Nonlinear Diffusion in Irregular Domains (U G Abdulla)Viscosity Lyapunov Functions for Almost Sure Stability of Degenerate Diffusions (M Bardi & A Cesaroni)Approximating Exterior Flows by Flows on Truncated Exterior Domains: Piecewise Polygonal Artificial Boundaries (P Deuring)Epidemic Models with Compartmental Diffusion (W E Fitzgibbon et al.)Exact Controllability of Piezoelectric Shells (B Miara)Bifurcation in Population Dynamics (K Umezu)and other papers Readership: Graduate students and researchers in the fields of partial differential equations and applied mathematics. Keywords:
Analytic Semigroups And Optimal Regularity In Parabolic Problems
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Author : Alessandra Lunardi
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-01-27
Analytic Semigroups And Optimal Regularity In Parabolic Problems written by Alessandra Lunardi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-27 with Mathematics categories.
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)
Proceedings Of The 4th European Conference Elliptic And Parabolic Problems
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Author : Josef Bemelmans
language : en
Publisher: World Scientific
Release Date : 2002
Proceedings Of The 4th European Conference Elliptic And Parabolic Problems written by Josef Bemelmans and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This book provides an overview of the state of the art in important subjects, including ? besides elliptic and parabolic issues ? geometry, free boundary problems, fluid mechanics, evolution problems in general, calculus of variations, homogenization, control, modeling and numerical analysis.
Recent Advances In Elliptic And Parabolic Problems
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Author : Chiun-Chuan Chen
language : en
Publisher: World Scientific
Release Date : 2005-02-24
Recent Advances In Elliptic And Parabolic Problems written by Chiun-Chuan Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-24 with Science categories.
The book is an account on recent advances in elliptic and parabolic problems and related equations, including general quasi-linear equations, variational structures, Bose-Einstein condensate, Chern–Simons model, geometric shell theory and stability in fluids. It presents very up-to-date research on central issues of these problems such as maximal regularity, bubbling, blowing-up, bifurcation of solutions and wave interaction. The contributors are well known leading mathematicians and prominent young researchers. The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings) • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings) • CC Proceedings — Engineering & Physical Sciences Contents:Maximal Regularity and Quasilinear Parabolic Boundary Value Problems (H Amann)Remarks on the Two and Three Membranes Problem (J-F Rodrigues et al.)Bubbling and Criticality in Two and Higher Dimensions (M del Pino & M Musso)Blow Up Solutions for a Liouville Equation with Singular Data (P Esposito)Problems in Unbounded Cylindrical Domains (P Guidotti)Entire Solutions of Some Reaction-Diffusion on Equations (J-S Guo)Some Abelian Gauge Field Theories in the Self-dual and Nonself-dual Cases (J Han & N Kim)Ginzburg–Landau Equations on Non-uniform Media (S Kosugi)Finding the Elasticae by Means of Geometric Gradient Flows (C-C Lin & H R Schwetlick)Free Work Identity and Nonlinear Instability in Fluids with Free Boundaries (M Padula)Complete and Energy Blow-up in Superlinear Parabolic Problems (P Quittner)Non-stabilizing Solutions for a Supercritical Semilinear Parabolic Equation (E Yanagida)and other papers Readership: Graduate students and researchers in partial differential equations and mathematical physics. Keywords:Elliptic Equations;Parabolic Problems;Nonlinear Analysis;Partial Differential EquationsKey Features:Presents up-to-date research in many important and hot topicsWritten by first class researchers in related fieldsContains rich models arising from different fields
Galerkin Finite Element Methods For Parabolic Problems
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Author : V. Thomee
language : en
Publisher: Lecture Notes in Mathematics
Release Date : 1984-03
Galerkin Finite Element Methods For Parabolic Problems written by V. Thomee and has been published by Lecture Notes in Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-03 with Mathematics categories.