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Zbl 0995.35035
Guo, Jong-Shenq; Guo, Yung-Jen L.
On a fast diffusion equation with source.
(English)
[J] Tohoku Math. J., II. Ser. 53, No.4, 571-579 (2001). ISSN 0040-8735

Summary: We study the positive solution of the Cauchy problem for the fast diffusion equation with source $$u_t=\Delta (u^m)+u^p, \quad x\in\bbfR^n,\ t>0.$$ We derive a secondary critical exponent of the behavior of the initial value at infinity for the existence of global (in time) and nonglobal solutions of the Cauchy problem. Furthermore, the large time behaviors of those global solutions are also studied.
MSC 2000:
*35K65 Parabolic equations of degenerate type
35B33 Critical exponents
35B40 Asymptotic behavior of solutions of PDE
35K15 Second order parabolic equations, initial value problems
35K55 Nonlinear parabolic equations
34B15 Nonlinear boundary value problems of ODE

Keywords: secondary critical exponent; large time behaviors

Cited in: Zbl 1054.35008

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