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Zbl 1227.35053
Mu, Chunlai; Zeng, Rong; Zhou, Shouming
Life span and a new critical exponent for a doubly degenerate parabolic equation with slow decay initial values.
(English)
[J] J. Math. Anal. Appl. 384, No. 2, 181-191 (2011). ISSN 0022-247X

Summary: We investigate the behavior of the positive solution of the Cauchy problem for the equation $$u_t- \text{div}\big(|\nabla u^m|^{p-2}\nabla u^m\big)=u^q$$ with 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 span of solutions are also studied.
MSC 2000:
*35B33 Critical exponents
35B44
35K65 Parabolic equations of degenerate type
35K59

Keywords: blow-up; global existence; critical exponent; large time behavior; life span; secondary critical exponent

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