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- Author: Atsushi Yagi
- Publisher: Springer
- ISBN-10: 981161895X
- ISBN-13: 9789811618956
- Format: 15.6 x 23.4 x 0.4 cm, minkšti viršeliai
- Language: English
- SAVE -10% with code: EXTRA
Abstract Parabolic Evolution Equations and Lojasiewicz-Simon Inequality I (e-book) (used book) | bookbook.eu
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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.
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- Author: Atsushi Yagi
- Publisher: Springer
- ISBN-10: 981161895X
- ISBN-13: 9789811618956
- Format: 15.6 x 23.4 x 0.4 cm, minkšti viršeliai
- Language: English English
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.
Reviews