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 $\frac{\partial u}{\partial t}-\text{div}(a(x,t,u,\mathrm{\nabla }u))-\text{div}\varphi (u)=f-\text{div}g$, where the main operator a(x,t,u,∇u)$a(x,t,u,\mathrm{\nabla }u)$ 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.