Secondary critical exponent,large time behavior and life span for a quasilinear parabolic equation with slowly decaying initial values |
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Authors: | Yongsheng Mi Chunlai Mu Rong Zeng |
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Affiliation: | 1.College of Mathematics and Statistics,Chongqing University,Chongqing,People’s Republic of China;2.College of Mathematics and Computer Sciences,Yangtze Normal University,Fuling, Chongqing,People’s Republic of China |
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Abstract: | In this paper, we consider the positive solution of the Cauchy problem for the following doubly degenerate parabolic equation $$u_t-{rm div}(|nabla u|^{p} nabla u^m)=u^q$$ with p > 0, q > 1, m > 1, and initial value decaying at infinity and give a new secondary critical exponent for the existence of global and nonglobal solutions. Furthermore, the large time behavior and the life spans of solutions are also studied. |
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