Nonlinear degenerate parabolic equations with measure data (Q1779854)

The author studies the solvability of the problem \(\partial u/\partial t+Au=f\) in \(\Omega\times(0,T)\), \(u=0\) on \(\partial\Omega\times(0,T)\), \(u(x,0)=u_0\) in \(\Omega\), where \(\Omega\) is a smooth bounded domain in \(\mathbb R^N\), \(N\geq2\), \(A\) is a non-uniformly elliptic operator of the form \(Au=-\text{div}\,(a(x,t,u,\nabla u))\) and \(f,u_0\) are bounded Radon measures. The proof is based on the approximation of \(f\) and \(u_0\) by smooth functions.