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Weighted Energy-Dissipation approach to semilinear gradient flows with state-dependent dissipation (2404.03370v1)
Published 4 Apr 2024 in math.AP
Abstract: We investigate the Weighted Energy-Dissipation variational approach to semilinear gradient flows with state-dependent dissipation. A family of parameter-dependent functionals defined over entire trajectories is introduced and proved to admit global minimizers. These global minimizers correspond to solutions of elliptic-in-time regularizations of the limiting causal problem. By passing to the limit in the parameter we prove that such global minimizers converge, up to subsequences, to a solution of the gradient flow.
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