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Blow-up, global existence and exponential decay estimates for a class of quasilinear parabolic problems. (English) Zbl 1158.35375
Summary: This paper deals with a class of nonlinear parabolic problems in divergence form whose solutions, without appropriate data restrictions, might blow up at some finite time. The purpose of this paper is to establish conditions on the data sufficient to guarantee blow-up of solution at some finite time $\tau $, conditions to ensure that the solution remains bounded as well as conditions to derive some explicit exponential decay bounds for the solution and its derivatives.

MSC:
35K55Nonlinear parabolic equations
35K20Second order parabolic equations, initial boundary value problems
35B40Asymptotic behavior of solutions of PDE
35B45A priori estimates for solutions of PDE
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References:
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