| Contents |
| We provide existence results for nonlinear diffusion equations with
multivalued time-dependent nonlinearities derived from convex l.s.c.
potentials, under minimal growth and coercivity conditions. Following a
variational principle, we prove 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 some cases, under further assumptions the null minimizer in the
minimization problem is found to coincide with a weak solution to the
nonlinear equation. Applications to various physical models (e.g.,
self-organized criticality) are discussed. |
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