This paper deals with critical exponents for a doubly degenerate nonlinear parabolic system coupled via local sources and with inner absorptions under null Dirichlet boundary conditions in a smooth bounded domain. The author first establishes the comparison principle and local existence theorem for the above problem. Then under appropriate hypotheses, the author proves that the solution either exists globally or blows up in finite time depends on the initial data and the relations of the parameters in the system. The critical exponent of the system is simply described via a characteristic matrix equation introduced. Keyword: Critical exponents; Doubly degenerate nonlinear parabolic system; Local sources; Inner absorptions; Global existence; Finite time blow-up. AMS(MOS). Mathematics Subject Classification: 35B35; 35K57; 35K60; 35K65.
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