Abstract Parabolic Evolution Equations and Lojasiewicz-Simon Inequality I

Abstract Theory
2021. Auflage 2021
ISBN: 978-981-16-1895-6
Verlag: Springer Nature Singapore

Buch, Englisch, 61 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 113 g

Reihe: SpringerBriefs in Mathematics

The classical Lojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the Lojasiewicz–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 Lojasiewicz–Simon gradient inequality.
In order to apply the abstract results to a wider class of concrete nonlinear parabolic equations, the usual Lojasiewicz–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.

Zielgruppe

Research

Autoren/Hrsg.

Yagi, Atsushi

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen

Inhaltsverzeichnis

1.Preliminary.- 2.Asymptotic Convergence.- 3.Extended Lojasiewicz–Simon Gradient Inequality.