Doubly Nonlinear Degenerate Parabolic Systems with Coupled Nonlinear Boundary Conditions

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In this paper, we study the global existence and the global nonexistence of doubly nonlinear degenerate parabolic systems with nonlinear boundary conditions. We first prove a local existence result by the regularization method. Next, we construct a weak comparison principle. Then we discuss the large time behavior of solutions by using a modified upper and lower solution methods and constructing various upper and lower solutions. Necessary and sufficient conditions on the global existence of all positive (weak) solutions are obtained. © 2002 Elsevier Science (USA).

Keywords: blow up in finite time.; doubly nonlinear degenerate parabolic systems; global solution; non-Newtonian flow; nonlinear boundary conditions

Document Type: Research Article

Affiliations: Department of Mathematics, Henan University, Kaifeng, 475001, People's Republic of China

Publication date: July 1, 2002

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