Abstract Parabolic Evolution Equations and Lojasiewicz–Simon Inequality I

The classical ?ojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the ?ojasiewicz–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 ?ojasiewicz–Simon gradient inequality.