Variational Solutions to Nonlinear Diffusion Equations with Singular Diffusivity

Gabriela Marinoschi ()
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Gabriela Marinoschi: Romanian Academy

Journal of Optimization Theory and Applications, 2014, vol. 161, issue 2, No 5, 430-445

Abstract: Abstract We provide existence results for nonlinear diffusion equations with multivalued time-dependent nonlinearities related to convex continuous not coercive potentials. The results in this paper, following a variational principle, state that a generalized solution of the nonlinear equation can be retrieved as a solution of an appropriate minimization problem for a convex functional involving the potential and its conjugate. In the not coercive case, this assertion is conditioned by the validity of a relation between the solution and the nonlinearity. A sufficient condition, under which this relation is true, is given. At the end, we present a discussion on the solution existence for a particular equation describing a self-organized criticality model.

Keywords: Variational methods; Brezis–Ekeland principle; Convex optimization problems; Nonlinear diffusion equations; Self-organized criticality; Sand-pile model (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10957-013-0430-5

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