The strong maximum principle in parabolic problems with the -Laplacian in a domain

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• 作者：Jiří ; Benedikt^a ; ^{benedikt@kma.zcu.cz" class="auth_mail" title="E-mail the corresponding author} ; Petr Girg^a ; ^{pgirg@kma.zcu.cz" class="auth_mail" title="E-mail the corresponding author} ; Luk&aacute ; &scaron ; Kotrla^a ; ^{kotrla@kma.zcu.cz" class="auth_mail" title="E-mail the corresponding author} ; Peter Tak&aacute ; č^b ; ^{peter.takac@uni-rostock.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Quasilinear parabolic equation ; Singular pp-Laplacian ; Subsolution ; Expanding spherical wave ; Comparison principle
• 刊名：Applied Mathematics Letters
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：63
• 期：Complete
• 页码：95-101
• 全文大小：578 K

文摘

We establish a strong maximum principle for a nonnegative continuous solution $u:\overline{\Omega }\times [0,T)\to {\mathbb{R}}_{+}$ of a doubly nonlinear parabolic problem in a space–time cylinder Ω×(0,τ)$\Omega \times (0,\tau )$ with a domain Ω⊂R^N$\Omega \subset {\mathbb{R}}^N$ and a sufficiently short time interval (0,τ)⊂(0,T)$(0,\tau )\subset (0,T)$. Our method takes advantage of a nonnegative subsolution derived from an expanding spherical wave.