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| A famous result of S. L ojasiewicz states that if $F:\mathbb{R}^d\to \mathbb{R}$ is real analytic, then every bounded solution $U$ of the gradient flow $U'(t)=-\nabla F(U(t))$
converges to a critical point of $F$ as $t\to +\infty$.
This convergence result has been generalized to a large variety of finite or infinite dimensional gradient-like flows.
In this talk, we show how some of these results can be adapted to time discretizations of gradient-like flows, in view of applications to Allen-Cahn, Cahn-Hilliard or phase-field crystal equations. |
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