Existence and uniqueness of solutions for a class of doubly degenerate parabolic equations

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• 作者：Weilin Zou ; ^{zwl267@163.com" class="auth_mail" title="E-mail the corresponding author} ; Juan Li ^{ttyyD114@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Doubly degenerate ; Existence and uniqueness ; Doubling variable method
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：446
• 期：2
• 页码：1833-1862
• 全文大小：493 K

文摘

In this paper, we study the Dirichlet problem for degenerate parabolic equations of the form class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305881&_mathId=si1.gif&_user=111111111&_pii=S0022247X16305881&_rdoc=1&_issn=0022247X&md5=64083fc48699b88d8b511c4e760b22ae">class="imgLazyJSB inlineImage" height="20" width="318" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16305881-si1.gif">class="mathContainer hidden">class="mathCode">$\frac{\partial u}{\partial t}-\text{div}(a(x,t,u,\mathrm{\nabla }u))-\text{div}\varphi (u)=f-\text{div}g$, where the main operator class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305881&_mathId=si2.gif&_user=111111111&_pii=S0022247X16305881&_rdoc=1&_issn=0022247X&md5=1adbcf93f7bb74310a52b227d2502aab" title="Click to view the MathML source">a(x,t,u,∇u)class="mathContainer hidden">class="mathCode">$a(x,t,u,\mathrm{\nabla }u)$ is allowed to degenerate with respect to the unknown u. Under suitable conditions on a and ϕ, we prove that there exists an unique solution u of this problem.