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} ; Luká ; &scaron ; Kotrla^a ; ^{kotrla@kma.zcu.cz" class="auth_mail" title="E-mail the corresponding author} ; Peter Taká ; 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 2117&_mathId=si2.gif&_user=111111111&_pii=S0893965916302117&_rdoc=1&_issn=08939659&md5=a0143cc5bc0cc05936d1b6c3a74f85a8">2117-si2.gif">$u:\overline{\Omega }\times [0,T)\to {\mathbb{R}}_{+}$ of a doubly nonlinear parabolic problem in a space–time cylinder 2117&_mathId=si3.gif&_user=111111111&_pii=S0893965916302117&_rdoc=1&_issn=08939659&md5=f0e0d75510035919c5958d14dca78fa0" title="Click to view the MathML source">Ω×(0,τ)$\Omega \times (0,\tau )$ with a domain 2117&_mathId=si4.gif&_user=111111111&_pii=S0893965916302117&_rdoc=1&_issn=08939659&md5=b7a31cd8f34c6c2003cae18af5aa9f8d" title="Click to view the MathML source">Ω⊂R^N$\Omega \subset {\mathbb{R}}^N$ and a sufficiently short time interval 2117&_mathId=si5.gif&_user=111111111&_pii=S0893965916302117&_rdoc=1&_issn=08939659&md5=00fe588b278a5af5d67a0fc537babd05" title="Click to view the MathML source">(0,τ)⊂(0,T)$(0,\tau )\subset (0,T)$. Our method takes advantage of a nonnegative subsolution derived from an expanding spherical wave.