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Article Dans Une Revue Nonlinear Differential Equations and Applications Année : 2010

Renormalized solution for Stefan type problems: existence and uniqueness

Résumé

We consider a class of nonlinear degenerate problems of Stefan type: $$u_t- \Delta w -\nabla F(u,w)= g(\cdot,u), \ w\in \beta(u)$$ where β is a maximal monotone graph in $${\mathbb{R}^2,}$$ with homogenous Dirichlet conditions and initial conditions. Under rather general assumptions on F and g, we prove existence and uniqueness of renormalized solutions.

Dates et versions

hal-00475849 , version 1 (23-04-2010)

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Noureddine Igbida, Karima Sbihi, Petra Wittbold. Renormalized solution for Stefan type problems: existence and uniqueness. Nonlinear Differential Equations and Applications, 2010, 17 (1), pp.69-93. ⟨10.1007/s00030-009-0040-y⟩. ⟨hal-00475849⟩
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