Existence of a renormalized solution of nonlinear parabolic equations with general measure data
Abstract
In this paper we prove the existence of a renormalized solution for nonlinear parabolic equations of the type:
$$\displaystyle{\partial b(x,u)
\over
\partial t} - {\rm div}\Big(a(x,t,\nabla u)\Big)=\mu\qquad \text{in}\ \Omega\times (0,T),$$ where the right hand
side is a general measure, $b(x,u)$ is an
unbounded function of $u$ and $- {\rm div}(a(x,t,\nabla u))$
is a Leray--Lions type operator with growth $|\nabla u|^{p-1}$ in
$\nabla u$.
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