We study the existence of solutions of a nonlinear parabolic problem of Cauchy-Dirichlet type having a lower order term which depends on the gradient. The model we have in mind is the following: $$ u_t-div (A(t,x)nabla u|nabla u|^{p-2})=gamma |Nabla u|^q+f(t,x) quad in quad Q_T, $$ $$ u=0 quad on quad(0,T) imes partial Omega, $$ u(0,x)=u_0(x) quad in quad Omega, $$ where $Q_T=(0,T) imes Omega$, $Omega$ is a bounded domain of $mathrm{R}^N$, $Nge 2$, $1<p></p>
Existence results for a Cauchy–Dirichlet parabolic problem with a repulsive gradient term / Magliocca, Martina. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 166:(2018), pp. 102-143. [10.1016/j.na.2017.09.012]
Existence results for a Cauchy–Dirichlet parabolic problem with a repulsive gradient term
Magliocca, Martina
2018
Abstract
We study the existence of solutions of a nonlinear parabolic problem of Cauchy-Dirichlet type having a lower order term which depends on the gradient. The model we have in mind is the following: $$ u_t-div (A(t,x)nabla u|nabla u|^{p-2})=gamma |Nabla u|^q+f(t,x) quad in quad Q_T, $$ $$ u=0 quad on quad(0,T) imes partial Omega, $$ u(0,x)=u_0(x) quad in quad Omega, $$ where $Q_T=(0,T) imes Omega$, $Omega$ is a bounded domain of $mathrm{R}^N$, $Nge 2$, $1| File | Dimensione | Formato | |
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