caa a22 4500 445843853 CHVBK 20180317145352.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s00526-010-0384-5 doi (NATIONALLICENCE)springer-10.1007/s00526-010-0384-5 Local estimates for parabolic equations with nonlinear gradient terms [Elektronische Daten] [Tommaso Leonori, Francesco Petitta] In this paper we deal with local estimates for parabolic problems in $${\mathbb{R}^N}$$ with absorbing first order terms, whose model is $$\left\{\begin{array}{l@{\quad}l}u_t- \Delta u +u |\nabla u|^q = f(t,x) \quad &{\rm in}\, (0,T) \times \mathbb{R}^N\,,\\u(0,x)= u_0 (x) &{\rm in}\, \mathbb{R}^N \,,\quad\end{array}\right.$$ where $${T >0 , \, N\geq 2,\, 1 < q \leq 2,\, f(t,x)\in L^1\left( 0,T; L^1_{\rm loc} \left(\mathbb{R}^N\right)\right)}$$ and $${u_0\in L^1_{\rm loc}\left(\mathbb{R}^{N}\right)}$$ . Springer-Verlag, 2010 Leonori Tommaso Departamento de Análisis Matemático, Universidad de Granada, 18071, Granada, Spain aut Petitta Francesco Departamento de Análisis Matemático, Universitat de Valencia, C/Dr. Moliner 50, 46100, Burjassot, Valencia, Spain aut Calculus of Variations and Partial Differential Equations Springer-Verlag 42/1-2(2011-09-01), 153-187 0944-2669 42:1-2<153 2011 42 526 https://doi.org/10.1007/s00526-010-0384-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00526-010-0384-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Leonori Tommaso Departamento de Análisis Matemático, Universidad de Granada, 18071, Granada, Spain aut NATIONALLICENCE 700 1- Petitta Francesco Departamento de Análisis Matemático, Universitat de Valencia, C/Dr. Moliner 50, 46100, Burjassot, Valencia, Spain aut NATIONALLICENCE 773 0- Calculus of Variations and Partial Differential Equations Springer-Verlag 42/1-2(2011-09-01), 153-187 0944-2669 42:1-2<153 2011 42 526 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer