Existence of capacity solution for a perturbed nonlinear coupled system

摘要

The aim of this paper is to show the existence of a capacity solution to a degenerate perturbed system involving an equation of parabolic type and an equation of elliptic type. This system may be regarded as a generalization version of the well-known thermistor problem; in this case, the unknowns are the temperature in a conductor and the electrical potential. We study the general case where the nonlinear elliptic operator in the parabolic equation is of the form Au=-div(a(x,t, del u)), A being a Leray-Lions operator, which includes the particular case of the p-Laplacian operator. The problem is also perturbed by a function satisfying a sign condition and without assuming any restriction on its growth.