# Nonlinear parabolic equations with soft measure data

## TL;DR

This paper establishes existence and uniqueness for nonlinear parabolic equations involving the p-Laplace operator with measure data, expanding the understanding of such equations with non-smooth inputs.

## Contribution

It proves existence and uniqueness results for nonlinear parabolic problems with measure data and analyzes their main properties.

## Key findings

- Existence of solutions under measure data conditions
- Uniqueness of solutions for the nonlinear parabolic problem
- Analysis of solution properties and behavior

## Abstract

In this paper we prove existence and uniqueness results for nonlinear parabolic problems with Dirichlet boundary values whose model is \[ \left\{ \begin{aligned} &b(u)_t-\Delta_{p}u=\mu\;\mbox{in }(0,T)\times\Omega,\\ &b(u(0,x))=b(u_{0})\;\mbox{in }\Omega,\\ &u(t,x)=0\;\mbox{on }(0,T)\times\partial\Omega. \end{aligned} \right. \] 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.