Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality I - Atsushi Yagi

Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality I

Abstract Theory

(Autor)

Buch | Softcover
61 Seiten
2021 | 1st ed. 2021
Springer Verlag, Singapore
978-981-16-1895-6 (ISBN)
69,54 inkl. MwSt
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.

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

Erscheinungsdatum
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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