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Zbl 1195.35068
Cianci, P.; Martynenko, A.V.; Tedeev, A.F.
The blow-up phenomenon for degenerate parabolic equations with variable coefficients and nonlinear source. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 7, 2310-2323 (2010). ISSN 0362-546X

Summary: The Cauchy problem for a degenerate parabolic equation with a source and variable coefficient of the form $$\frac {\partial u}{\partial t} = div (\rho(x) u^{m-1} |Du|^{\lambda -1} Du) + u^p$$ is studied. Global in time existence and nonexistence conditions are found for a solution to the Cauchy problem. Exact estimates of a solution are obtained in the case of global solvability. A sharp universal (i.e., independent of the initial function) estimate of a solution near the blow-up time is obtained.

MSC 2000:: *35B44
35K65 Parabolic equations of degenerate type
35K15 Second order parabolic equations, initial value problems
35K59

Keywords: existence and nonexistence theorems

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