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Zbl 1182.35028
Mu, Chunlai; Li, Yuhuan; Wang, Ying
Life span and a new critical exponent for a quasilinear degenerate parabolic equation with slow decay initial values. (English)
[J] Nonlinear Anal., Real World Appl. 11, No. 1, 198-206 (2010). ISSN 1468-1218

Summary: We consider the positive solution of a Cauchy problem for the following $p$-Laplace parabolic equation $$u_t = \text{div}(|\nabla u|^{p-2}\nabla u)+u^q,\quad p>2,\ q>1,$$ and give a secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence of global and non-global solutions of the Cauchy problem. Furthermore, the life span of solutions is also studied.

MSC 2000:: *35B33 Critical exponents
35K65 Parabolic equations of degenerate type
35B44
35K92
35K15 Second order parabolic equations, initial value problems

Keywords: slowly decay initial data

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