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Zbl 1066.35047
Li, Yuhuan; Mu, Chunlai
Life span and a new critical exponent for a degenerate parabolic equation. (English)
[J] J. Differ. Equations 207, No. 2, 392-406 (2004). ISSN 0022-0396

Summary: We consider the positive solution of the Cauchy problem for the equation $$u_t=u^p\Delta u+u^q,\quad p>1,\ q>1$$ and give a secondary critical exponent of the behavior of initial value at infinity for the existence of global and nonglobal solutions of the Cauchy problem. Furthermore, the life span of solutions are also studied.

MSC 2000:: *35K65 Parabolic equations of degenerate type
35K55 Nonlinear parabolic equations
35K15 Second order parabolic equations, initial value problems
35B33 Critical exponents
35B40 Asymptotic behavior of solutions of PDE

Keywords: Blow-up; Life span; Global existence; Critical exponent; Degenerate parabolic equation; Slowly decaying initial data; Self-solution

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Zentralblatt MATH Berlin [Germany]