Existence of solution for a class of heat equation involving the 1-Laplacian operator

Abstract

This paper concerns the existence of global solutions for the following class of heat equations involving the 1-Laplacian operator for the Dirichlet problem {ut−Δ1u=f(u)inΩ×(0,+∞),u=0in∂Ω×(0,+∞),u(x,0)=u0(x)inΩ, where Ω⊂RN is a smooth bounded domain, N≥1, f:R→R is a continuous function satisfying some technical conditions and [Formula presented] denotes the 1-Laplacian operator. The existence of global solutions is done by using an approximation technique that consists in working with a class of p-Laplacian problems associated with (P) and then taking the limit when p→1+ to get our results