Abstract Parabolic Evolution Equations and ojasiewicz Simon Inequality I

This book presents a unified method to show asymptotic convergence of solutions to a stationary solution for abstract parabolic evolution equations of the gradient form by utilizing this Łojasiewicz–Simon gradient inequality.

Abstract Parabolic Evolution Equations and   ojasiewicz   Simon Inequality I

The classical Łojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the Łojasiewicz–Simon gradient inequality. This book presents a unified method to show asymptotic convergence of solutions to a stationary solution for abstract parabolic evolution equations of the gradient form by utilizing this Łojasiewicz–Simon gradient inequality. In order to apply the abstract results to a wider class of concrete nonlinear parabolic equations, the usual Łojasiewicz–Simon inequality is extended, which is published here for the first time. In the second version, these abstract results are applied to reaction–diffusion equations with discontinuous coefficients, reaction–diffusion systems, and epitaxial growth equations. The results are also applied to the famous chemotaxis model, i.e., the Keller–Segel equations even for higher-dimensional ones.

More Books:

Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality I
Language: en
Pages: 61
Authors: Atsushi Yagi
Categories: Mathematics
Type: BOOK - Published: 2021-05-31 - Publisher: Springer Nature

The classical Łojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the Łojasiewicz–Simon gradient inequality. This book presents a unified method to show asymptotic convergence of solutions to a stationary solution for abstract parabolic evolution equations of the gradient form by utilizing this Łojasiewicz–Simon
Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality II
Language: en
Pages: 128
Authors: Atsushi Yagi
Categories: Mathematics
Type: BOOK - Published: 2021-08-12 - Publisher: Springer Nature

This second volume continues the study on asymptotic convergence of global solutions of parabolic equations to stationary solutions by utilizing the theory of abstract parabolic evolution equations and the Łojasiewicz–Simon gradient inequality. In the first volume of the same title, after setting the abstract frameworks of arguments, a general convergence
Abstract Parabolic Evolution Equations and Łojasiewicz-Simon Inequality I
Language: en
Pages: 68
Authors: Atsushi Yagi
Categories: Differential equations, Parabolic
Type: BOOK - Published: 2021 - Publisher:

The classical ojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the ojasiewiczSimon gradient inequality. This book presents a unified method to show asymptotic convergence of solutions to a stationary solution for abstract parabolic evolution equations of the gradient form by utilizing this ojasiewiczSimon
Nonlinear Evolution Equations and Related Topics
Language: en
Pages: 807
Authors: Wolfgang Arendt, Haim Brezis, Michel Pierre
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Birkhäuser

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
Evolution Equations and Their Applications in Physical and Life Sciences
Language: en
Pages: 530
Authors: G Lumer
Categories: Mathematics
Type: BOOK - Published: 2019-04-24 - Publisher: CRC Press

This volume presents a collection of lectures on linear partial differntial equations and semigroups, nonlinear equations, stochastic evolutionary processes, and evolution problems from physics, engineering and mathematical biology. The contributions come from the 6th International Conference on Evolution Equations and Their Applications in Physica