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The blow-up phenomenon for degenerate parabolic equations with variable coefficients and nonlinear source. (English) Zbl 1195.35068

Summary: The Cauchy problem for a degenerate parabolic equation with a source and variable coefficient of the form

u t=div(ρ(x)u m-1 |Du| λ-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:
35B44Blow-up (PDE)
35K65Parabolic equations of degenerate type
35K15Second order parabolic equations, initial value problems
35K59Quasilinear parabolic equations