Local estimates for parabolic equations with nonlinear gradient terms

Abstract

In this paper we deal with local estimates for parabolic problems in ${\mathbb{R}}^N$ with absorbing first order terms, whose model is $\{ {l} u_t- Δu +u |\nabla u|^q = f(t,x) \quad &{in}\, (0,T) \times \mathbb{R}^N\,, \\[1.5 ex] u(0,x)= u_0 (x) &box{in}\, \mathbb{R}^N.$ where $T>0$, $N\ge 2$, $1<q\le 2$, $f(t,x)\in L^1(0,T;L_{\mathrm{loc}}^1({\mathbb{R}}^N))$ and $u_0\in L_{\mathrm{loc}}^1({\mathbb{R}}^N)$.

References in corpus (1)

• Renormalized solutions of nonlinear parabolic equations with general measure data