Nonlinear evolution problems with singular coefficients in the lower order terms

TL;DR

This paper studies a quasilinear parabolic PDE with singular coefficients in lower order terms, proving existence of solutions and analyzing their long-term behavior in an infinite time horizon setting.

Contribution

It introduces new existence results for nonlinear evolution equations with singular lower order coefficients and characterizes the solutions' asymptotic behavior over infinite time.

Findings

Existence of solutions to the PDE with singular coefficients

Description of long-term behavior of solutions

Framework for handling singular lower order terms in parabolic equations

Abstract

We consider a Cauchy Dirichlet problem for a quasilinear second order parabolic equation with lower order term driven by a singular coefficient. We establish an existence result to such a problem and we describe the time behavior of the solution in the case of the infinite time horizon.