Equivalence between entropy and renormalized solutions for parabolic equations with smooth measure data

Abstract

We consider the nonlinear heat equation (with Leray-Lions operators) on an open bounded subset of R N with Dirichlet homogeneous boundary conditions. The initial condition is in L 1 and the right hand side is a smooth measure. We extend a previous notion of entropy solutions and prove that they coincide with the renormalized solutions. © 2007 Birkhäuser Verlag.