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Global existence and nonexistence for degenerate parabolic systems
Authors:Yuxiang Li  Weibing Deng  Chunhong Xie
Institution:Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China ; Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China

Chunhong Xie ; Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China

Abstract:The initial-boundary value problems are considered for the strongly coupled degenerate parabolic system

\begin{displaymath}\begin{split} u_t=v^p(\Delta u+au), v_t=u^q(\Delta v+bv) \end{split}\end{displaymath}

in the cylinder $\Omega\times(0,\infty)$, where $\Omega\subset R^N$ is bounded and $p, q, a, b$ are positive constants. We are concerned with the global existence and nonexistence of the positive solutions. Denote by $\lambda_1$ the first Dirichlet eigenvalue for the Laplacian on $\Omega$. We prove that there exists a global solution iff $\lambda_1\geq \min\{a,b\}$.

Keywords:Global existence  global nonexistence  degenerate parabolic system
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