January  1996, 2(1): 23-52. doi: 10.3934/dcds.1996.2.23

Evolution equations governed by the subdifferential of a convex composite function in finite dimensional spaces

1. 

Departement de mathematiques, Universite Montpellier II, 34095 Montpellier cedex 5, France

Received  October 1995 Published  October 1995

Under quite general assumptions, we prove existence, uniqueness and regularity of a solution $U$ to the evolution equation $-U'(t)\in\partial(g\circ F)(U(t))$, $U(0)=u_0$, where $g:\mathbb{R}^q\rightarrow\mathbb{R}\cup\{+\infty\}$ is a closed proper convex function, $F:\mathbb{R}^p\rightarrow \mathbb{R}^q$ is a continuously differentiable mapping whose gradient is Lipschitz continuous on bounded subsets and $u_0\in\dom (g\circ F)$. We also study the asymptotic behavior of $U$ and give an application to nonlinear mathematical programming.
Citation: Sophie Guillaume. Evolution equations governed by the subdifferential of a convex composite function in finite dimensional spaces. Discrete & Continuous Dynamical Systems - A, 1996, 2 (1) : 23-52. doi: 10.3934/dcds.1996.2.23
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