Nonlinear Parabolic Equations And Hyperbolic Parabolic Coupled Systems
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Nonlinear Parabolic Equations And Hyperbolic Parabolic Coupled Systems
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Author : Songmu Zheng
language : en
Publisher: CRC Press
Release Date : 2020-05-05
Nonlinear Parabolic Equations And Hyperbolic Parabolic Coupled Systems written by Songmu Zheng and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-05 with Mathematics categories.
This monograph is devoted to the global existence, uniqueness and asymptotic behaviour of smooth solutions to both initial value problems and initial boundary value problems for nonlinear parabolic equations and hyperbolic parabolic coupled systems. Most of the material is based on recent research carried out by the author and his collaborators. The book can be divided into two parts. In the first part, the results on decay of solutions to nonlinear parabolic equations and hyperbolic parabolic coupled systems are obtained, and a chapter is devoted to the global existence of small smooth solutions to fully nonlinear parabolic equations and quasilinear hyperbolic parabolic coupled systems. Applications of the results to nonlinear thermoelasticity and fluid dynamics are also shown. Some nonlinear parabolic equations and coupled systems arising from the study of phase transitions are investigated in the second part of the book. The global existence, uniqueness and asymptotic behaviour of smooth solutions with arbitrary initial data are obtained. The final chapter is further devoted to related topics: multiplicity of equilibria and the existence of a global attractor, inertial manifold and inertial set. A knowledge of partial differential equations and Sobolev spaces is assumed. As an aid to the reader, the related concepts and results are collected and the relevant references given in the first chapter. The work will be of interest to researchers and graduate students in pure and applied mathematics, mathematical physics and applied sciences.
Nonlinear Parabolic Hyperbolic Coupled Systems And Their Attractors
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Author : Yuming Qin
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-25
Nonlinear Parabolic Hyperbolic Coupled Systems And Their Attractors written by Yuming Qin 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 2008-11-25 with Mathematics categories.
This book presents recent results concerning the global existence in time, the large-time behavior, decays of solutions and the existence of global attractors for nonlinear parabolic-hyperbolic coupled systems of evolutionary partial differential equations.
Global Well Posedness Of Nonlinear Parabolic Hyperbolic Coupled Systems
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Author : Yuming Qin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-02-28
Global Well Posedness Of Nonlinear Parabolic Hyperbolic Coupled Systems written by Yuming Qin 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 2012-02-28 with Mathematics categories.
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.
Nonlinear Parabolic Equations And Hyperbolic Parab Olic Coupled Systems Pitman Monographs 76
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Author : Songmu Zheng
language : en
Publisher: Longman Sc & Tech
Release Date : 1995-04-01
Nonlinear Parabolic Equations And Hyperbolic Parab Olic Coupled Systems Pitman Monographs 76 written by Songmu Zheng and has been published by Longman Sc & Tech this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-04-01 with Mathematics categories.
Nonlinear Second Order Parabolic Equations
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Author : Mingxin Wang
language : en
Publisher: CRC Press
Release Date : 2021-05-12
Nonlinear Second Order Parabolic Equations written by Mingxin Wang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-12 with Mathematics categories.
The parabolic partial differential equations model one of the most important processes in the real-world: diffusion. Whether it is the diffusion of energy in space-time, the diffusion of species in ecology, the diffusion of chemicals in biochemical processes, or the diffusion of information in social networks, diffusion processes are ubiquitous and crucial in the physical and natural world as well as our everyday lives. This book is self-contained and covers key topics such as the Lp theory and Schauder theory, maximum principle, comparison principle, regularity and uniform estimates, initial-boundary value problems of semilinear parabolic scalar equations and weakly coupled parabolic systems, the upper and lower solutions method, monotone properties and long-time behaviours of solutions, convergence of solutions and stability of equilibrium solutions, global solutions and finite time blowup. It also touches on periodic boundary value problems, free boundary problems, and semigroup theory. The book covers major theories and methods of the field, including topics that are useful but hard to find elsewhere. This book is based on tried and tested teaching materials used at the Harbin Institute of Technology over the past ten years. Special care was taken to make the book suitable for classroom teaching as well as for self-study among graduate students. About the Author: Mingxin Wang is Professor of Mathematics at Harbin Institute of Technology, China. He has published ten monographs and textbooks and 260 papers. He is also a supervisor of 30 PhD students.
Nonlinear Parabolic And Elliptic Equations
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Author : C.V. Pao
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Parabolic And Elliptic Equations written by C.V. Pao 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 2012-12-06 with Mathematics categories.
In response to the growing use of reaction diffusion problems in many fields, this monograph gives a systematic treatment of a class of nonlinear parabolic and elliptic differential equations and their applications these problems. It is an important reference for mathematicians and engineers, as well as a practical text for graduate students.
Linear And Nonlinear Parabolic Complex Equations
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Author : Guo Chun Wen
language : en
Publisher: World Scientific
Release Date : 1999-04-29
Linear And Nonlinear Parabolic Complex Equations written by Guo Chun Wen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-04-29 with Mathematics categories.
This book deals mainly with linear and nonlinear parabolic equations and systems of second order. It first transforms the real forms of parabolic equations and systems into complex forms, and then discusses several initial boundary value problems and Cauchy problems for quasilinear and nonlinear parabolic complex equations of second order with smooth coefficients or measurable coefficients. Parabolic complex equations are discussed in the nonlinear case and the boundary conditions usually include the initial irregular oblique derivative. The boundary value problems are considered in multiply connected domains and several methods are used.
Nonlinear Parabolic Equations
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Author : Lucio Boccardo
language : en
Publisher: Longman Scientific and Technical
Release Date : 1987
Nonlinear Parabolic Equations written by Lucio Boccardo and has been published by Longman Scientific and Technical this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
Handbook Of Differential Equations Evolutionary Equations
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Author : C.M. Dafermos
language : en
Publisher: Elsevier
Release Date : 2004-08-24
Handbook Of Differential Equations Evolutionary Equations written by C.M. Dafermos and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-24 with Mathematics categories.
This book contains several introductory texts concerning the main directions in the theory of evolutionary partial differential equations. The main objective is to present clear, rigorous, and in depth surveys on the most important aspects of the present theory. The table of contents includes: W.Arendt: Semigroups and evolution equations: Calculus, regularity and kernel estimates A.Bressan: The front tracking method for systems of conservation laws E.DiBenedetto, J.M.Urbano,V.Vespri: Current issues on singular and degenerate evolution equations; L.Hsiao, S.Jiang: Nonlinear hyperbolic-parabolic coupled systems A.Lunardi: Nonlinear parabolic equations and systems D.Serre:L1-stability of nonlinear waves in scalar conservation laws B.Perthame:Kinetic formulations of parabolic and hyperbolic PDE’s: from theory to numerics
Non Resonant Solutions In Hyperbolic Parabolic Systems With Periodic Forcing
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Author : Aday Celik
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2020-09-30
Non Resonant Solutions In Hyperbolic Parabolic Systems With Periodic Forcing written by Aday Celik and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-30 with Mathematics categories.
This thesis is a mathematical investigation of damping effects in hyperbolic systems. In the first part two models from nonlinear acoustics are studied. Existence of time-periodic solutions to the Blackstock-Crighton equation and the Kuznetsov equation are established for time-periodic data sufficiently restricted in size. This leads to the conclusion that the dissipative effects in these models are sufficient to avoid resonance. In the second part the interaction of a viscous fluid with an elastic structure is studied. A periodic cell structure filled with a viscous fluid interacting with a deformable boundary of the cell is considered under time-periodic forcing. The motion of the fluid is governed by the Navier-Stokes equations and the deformable boundary is governed by the plate equation. It is shown that the damping mechanism induced by the viscous fluid is sufficient to avoid resonance in the elastic structure.