Existence for weakly coercive nonlinear diffusion equations via a variational principle

Gabriela Marinoschi

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arXiv · 1307.1881

Existence for weakly coercive nonlinear diffusion equations via a variational principle

Gabriela Marinoschi

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Abstract

We are concerned with the study of the well-posedness of a nonlinear diffusion equation with a monotonically increasing multivalued time-dependent nonlinearity derived from a convex continuous potential having a superlinear growth to infinity. The results in this paper state that the solution of the nonlinear equation can be retrieved as the null minimizer of an appropriate minimization problem for a convex functional involving the potential and its conjugate. This approach, inspired by the Brezis-Ekeland variational principle, provides new existence results under minimal growth and coercivity conditions.

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Gabriela Marinoschi. 2013-07-07. Existence for weakly coercive nonlinear diffusion equations via a variational principle. https://arxiv.org/abs/1307.1881

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