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On a fast diffusion equation with source. (English) Zbl 0995.35035

Summary: We study the positive solution of the Cauchy problem for the fast diffusion equation with source

u t =Δ(u m )+u p ,x 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:
35K65Parabolic equations of degenerate type
35B33Critical exponents (PDE)
35B40Asymptotic behavior of solutions of PDE
35K15Second order parabolic equations, initial value problems
35K55Nonlinear parabolic equations
34B15Nonlinear boundary value problems for ODE