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arXiv · 1411.2545

Local estimates for parabolic equations with nonlinear gradient terms

Tommaso Leonori·Francesco Petitta
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Abstract

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

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Tommaso Leonori, Francesco Petitta. 2014-11-10. Local estimates for parabolic equations with nonlinear gradient terms. https://doi.org/10.1007/s00526-010-0384-5

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