Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality I
Abstract Theory
Seiten
2021
|
1st ed. 2021
Springer Verlag, Singapore
978-981-16-1895-6 (ISBN)
Springer Verlag, Singapore
978-981-16-1895-6 (ISBN)
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.
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.
1.Preliminary.- 2.Asymptotic Convergence.- 3.Extended Łojasiewicz–Simon Gradient Inequality.
| Erscheinungsdatum | 07.06.2021 |
|---|---|
| Reihe/Serie | SpringerBriefs in Mathematics |
| Zusatzinfo | 17 Illustrations, black and white; X, 61 p. 17 illus. |
| Verlagsort | Singapore |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 981-16-1895-X / 981161895X |
| ISBN-13 | 978-981-16-1895-6 / 9789811618956 |
| Zustand | Neuware |
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