A Stationary Stefan Problem with Convection and Nonlinear Diffusion

José Miguel Urbano

Abstract: We consider a stationary two-phase Stefan problem with prescribed convection and prove existence of bounded solutions. The main features of this problem are a nonlinear constitutive law of diffusion involving the $p$-Laplacian and a discontinuous nonlinearity in the convection term due to the change of phase. The basic approach consists of using monotonicity techniques and an extended weak maximum principle.

Keywords: Free boundary problems; Stefan problem; $p$-Laplacian; monotonicity.

Classification (MSC2000): 35D05, 35J25, 35R35, 80A22

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