Global and nonglobal weak solutions to a degenerate parabolic system |
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| Authors: | Peidong Lei Sining Zheng |
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| Affiliation: | a Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, People's Republic of China
b Department of Mathematics, Northeast Normal University, Changchun 130024, People's Republic of China |
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| Abstract: | This paper deals with a degenerate parabolic system coupled via general reaction terms of power type. Global weak solutions are obtained by means of energy estimates and the De Giorgi's technique. In particular, the criterion for global nonexistence of weak solutions is proved by introducing suitable weak sub-solutions together with a weak comparison principle. In summary, the critical exponent for weak solutions of the degenerate parabolic system is determined. |
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| Keywords: | Degenerate parabolic systems Weak sub-solutions Weak super solutions Blow-up Global existence Characteristic algebraic system Critical exponent |
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