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 class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002203961500649X&_mathId=si1.gif&_user=111111111&_pii=S002203961500649X&_rdoc=1&_issn=00220396&md5=723a8873b9d8254d9e4e4c9f26ee90ef">class="imgLazyJSB inlineImage" height="25" width="31" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S002203961500649X-si1.gif">class="mathContainer hidden">class="mathCode">$W_{q^{\prime }}^{2,1}$-capacity, where class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002203961500649X&_mathId=si2.gif&_user=111111111&_pii=S002203961500649X&_rdoc=1&_issn=00220396&md5=ea17847c02390f11fa949855efbe313e">class="imgLazyJSB inlineImage" height="21" width="60" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S002203961500649X-si2.gif">class="mathContainer hidden">class="mathCode">$q^{\prime }=\frac{q}{q-1}$ and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002203961500649X&_mathId=si197.gif&_user=111111111&_pii=S002203961500649X&_rdoc=1&_issn=00220396&md5=f7b85e4bc24615b326c7c91fd9099c65" title="Click to view the MathML source">q>1class="mathContainer hidden">class="mathCode">$q>1$, for the existence of large solutions to equation class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002203961500649X&_mathId=si4.gif&_user=111111111&_pii=S002203961500649X&_rdoc=1&_issn=00220396&md5=7173c3b197c9321e7aff054760fa5f34" title="Click to view the MathML source">∂_tu−Δu+u^q=0class="mathContainer hidden">class="mathCode">${\partial }_{t}u-\mathrm{\Delta }u+u^q=0$ in a non-cylindrical domain. We provide also a sufficient condition for the existence of such solutions to equation class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002203961500649X&_mathId=si5.gif&_user=111111111&_pii=S002203961500649X&_rdoc=1&_issn=00220396&md5=562f93e6f9be9d7567ef5c5ba0ee8f51" title="Click to view the MathML source">∂_tu−Δu+e^u−1=0class="mathContainer hidden">class="mathCode">${\partial }_{t}u-\mathrm{\Delta }u+e^u-1=0$. Besides, we apply our results to equation: class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002203961500649X&_mathId=si6.gif&_user=111111111&_pii=S002203961500649X&_rdoc=1&_issn=00220396&md5=0319dc8214c7825ccf51d717c656e536" title="Click to view the MathML source">∂_tu−Δu+a|∇u|^p+bu^q=0class="mathContainer hidden">class="mathCode">${\partial }_{t}u-\mathrm{\Delta }u+a{|\mathrm{\nabla }u|}^p+b{u}^q=0$ for class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002203961500649X&_mathId=si120.gif&_user=111111111&_pii=S002203961500649X&_rdoc=1&_issn=00220396&md5=1f0a153f8f24219818bb127a1b36292c" title="Click to view the MathML source">a,b>0class="mathContainer hidden">class="mathCode">$a,b>0$, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002203961500649X&_mathId=si8.gif&_user=111111111&_pii=S002203961500649X&_rdoc=1&_issn=00220396&md5=bc7d94938636533830c19e9f423a0595" title="Click to view the MathML source">1<p<2class="mathContainer hidden">class="mathCode">$1<p<2$ and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002203961500649X&_mathId=si197.gif&_user=111111111&_pii=S002203961500649X&_rdoc=1&_issn=00220396&md5=f7b85e4bc24615b326c7c91fd9099c65" title="Click to view the MathML source">q>1class="mathContainer hidden">class="mathCode">$q>1$.