TY  - GEN
N2  - 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.
DO  - 10.1007/978-981-16-1896-3
DO  - doi
AB  - 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.
T1  - Abstract Parabolic Evolution Equations and Łojasiewicz-Simon Inequality I :Abstract Theory /
AU  - Yagi, Atsushi,
CN  - QA377.3
ID  - 1437144
KW  - Evolution equations.
KW  - Differential equations, Parabolic.
KW  - Équations d'évolution.
KW  - Équations différentielles paraboliques.
SN  - 9789811618963
SN  - 9811618968
SN  - 9789811618970
SN  - 9811618976
TI  - Abstract Parabolic Evolution Equations and Łojasiewicz-Simon Inequality I :Abstract Theory /
LK  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-981-16-1896-3
UR  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-981-16-1896-3
ER  -