On uniqueness of large solutions of nonlinear parabolic equations in nonsmooth domains

Details On uniqueness of large solutions of nonlinear parabolic equations in nonsmooth domains On uniqueness of large solutions of nonlinear parabolic equations in nonsmooth domains

2008-07-20

arxiv.org/abs/0807.3177v2

Mathematics

Analysis of PDEs

16 pages

Scientific paper

We study the existence and uniqueness of the positive solutions of the problem (P): $\partial_tu-\Delta u+u^q=0$ ($q>1$) in $\Omega\times (0,\infty)$, $u=\infty$ on $\partial\Omega\times (0,\infty)$ and $u(.,0)\in L^1(\Omega)$, when $\Omega$ is a bounded domain in $\mathbb R^N$. We construct a maximal solution, prove that this maximal solution is a large solution whenever $q

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