The blow-up phenomenon for degenerate parabolic equations with variable coefficients and nonlinear source

The Cauchy problem for a degenerate parabolic equation with a source and variable coefficient of the form ∂ u ∂ t = d i v ( ρ ( x ) u m − 1 | D u | λ − 1 D u ) + u p is studied. Global in time existence and nonexistence conditions are found for a solution to the Cauchy problem. Exact estimates of a...

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Bibliographic Details
Published in:Nonlinear analysis 2010-10, Vol.73 (7), p.2310-2323
Main Authors: Cianci, P., Martynenko, A.V., Tedeev, A.F.
Format: Article
Language:English
Subjects:
Blow-up solution
Cauchy problem
Degenerate parabolic equation
Estimates
Exact sciences and technology
Existence and nonexistence theorems
Mathematical analysis
Mathematics
Nonlinearity
Partial differential equations
Sciences and techniques of general use
Source term
Variable coefficients
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Summary:The Cauchy problem for a degenerate parabolic equation with a source and variable coefficient of the form ∂ u ∂ t = d i v ( ρ ( x ) u m − 1 | D u | λ − 1 D u ) + 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.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2010.06.026