We consider a class of Stefan-type problems having a convection term and a pseudomonotone nonlinear diffusion operator. Assuming data in L-1, we prove existence, uniqueness and stability in the framework of renormalized solutions. Existence is established from compactness and monotonicity arguments which yield stability of solutions with respect to L-1 convergence of the data. Uniqueness is proved through a classical L-1-contraction principle, obtained by a refinement of the doubling variable technique which allows us to extend previous results to a more general class of nonlinear possibly degenerate operators. (C) 2004 Elsevier Inc. All rights reserved.
Blanchard, D., Porretta, A. (2005). Stefan problems with nonlinear diffusion and convection. JOURNAL OF DIFFERENTIAL EQUATIONS, 210(2), 383-428 [10.1016/j.jde.2004.06.012].
Stefan problems with nonlinear diffusion and convection
PORRETTA, ALESSIO
2005-01-01
Abstract
We consider a class of Stefan-type problems having a convection term and a pseudomonotone nonlinear diffusion operator. Assuming data in L-1, we prove existence, uniqueness and stability in the framework of renormalized solutions. Existence is established from compactness and monotonicity arguments which yield stability of solutions with respect to L-1 convergence of the data. Uniqueness is proved through a classical L-1-contraction principle, obtained by a refinement of the doubling variable technique which allows us to extend previous results to a more general class of nonlinear possibly degenerate operators. (C) 2004 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
