Wiener criteria for existence of large solutions of nonlinear parabolic equations with absorption in a non-cylindrical domain

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• 作者：Quoc-Hung Nguyen ^{Hung.Nguyen-Quoc@lmpt.univ-tours.fr" class="auth_mail" title="E-mail the corresponding author quoc-hung.nguyen@epfl.ch" class="auth_mail" title="E-mail the corresponding author} ; Laurent Vé ; ron ; ^{Laurent.Veron@lmpt.univ-tours.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35K58 ; 28A12 ; 46E35
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：5 March 2016
• 年：2016
• 卷：260
• 期：5
• 页码：4805-4844
• 全文大小：446 K

文摘

We obtain a necessary condition and a sufficient condition, both expressed in terms of Wiener type tests involving the parabolic $W_{q^{\prime }}^{2,1}$-capacity, where and q>1$q>1$, for the existence of large solutions to equation ∂_tu−Δu+u^q=0${\partial }_{t}u-\mathrm{\Delta }u+u^q=0$ in a non-cylindrical domain. We provide also a sufficient condition for the existence of such solutions to equation ∂_tu−Δu+e^u−1=0${\partial }_{t}u-\mathrm{\Delta }u+e^u-1=0$. Besides, we apply our results to equation: ∂_tu−Δu+a|∇u|^p+bu^q=0${\partial }_{t}u-\mathrm{\Delta }u+a{|\mathrm{\nabla }u|}^p+b{u}^q=0$ for a,b>0$a,b>0$, 1<p<2$1<p<2$ and q>1$q>1$.