Nonlinear parabolic equations with soft measure data

Abstract

In this paper we prove existence and uniqueness results for nonlinear parabolic problems with Dirichlet boundary values whose model is \[ \left\{ \begin{aligned} &b(u)_t-Δ_{p}u=μ\;\mbox{in }(0,T)\timesΩ,\\ &b(u(0,x))=b(u_{0})\;\mbox{in }Ω,\\ &u(t,x)=0\;\mbox{on }(0,T)\times\partialΩ. \end{aligned} \right. \] where ${\Delta }_{p}u=\text{div}(|\nabla u{|}^{p-2}\nabla u)$ is the usual $p-$Laplace operator, $b$ is a increasing $C^1-$function and $\mu$ is a finite measure which does not charge sets of zero parabolic $p-$capacity, and we discuss their main properties.

arXiv admin note: text overlap with arXiv:1506.03671, arXiv:1708.04744 by other authors