Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality I (eBook)

Abstract Theory

Atsushi Yagi (Autor)

eBook Download: PDF

2021 | 1st ed. 2021
61 Seiten
Springer Singapore (Verlag)
978-981-16-1896-3 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 31.5.2021
• Reihe/Serie: SpringerBriefs in Mathematics
• Reihe/Serie: SpringerBriefs in Mathematics
• Zusatzinfo: X, 61 p. 17 illus.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Schlagworte: abstract parabolic evolution equations • Asymptotic Convergence of Solutions • Keller--Segel Equations • Łojasiewicz--Simon Inequality • Partial differential equations • Semilinear parabolic equations
• ISBN-10: 981-16-1896-8 / 9811618968
• ISBN-13: 978-981-16-1896-3 / 9789811618963