Doubly Nonlinear Degenerate Parabolic Systems with Coupled Nonlinear Boundary Conditions |
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Authors: | Shu Wang |
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Institution: | Department of Mathematics, Henan University, Kaifeng, 475001, People's Republic of China Institute of Mathematics, Academy of Mathematics and Systems Sciences, The Chinese Academy of Sciences, Beijing, 100080, People's Republic of Chinaf1wangshu@math03.math.ac.cnf1 |
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Abstract: | 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. |
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Keywords: | doubly nonlinear degenerate parabolic systems nonlinear boundary conditions non-Newtonian flow global solution blow up in finite time |
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