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Life span and a new critical exponent for a quasilinear degenerate parabolic equation with slow decay initial values. (English) Zbl 1182.35028

Summary: We consider the positive solution of a Cauchy problem for the following p-Laplace parabolic equation

u t =div(|u| p-2 u)+u q ,p>2,q>1,

and give a secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence of global and non-global solutions of the Cauchy problem. Furthermore, the life span of solutions is also studied.

MSC:
35B33Critical exponents (PDE)
35K65Parabolic equations of degenerate type
35B44Blow-up (PDE)
35K92Quasilinear parabolic equations with p-Laplacian
35K15Second order parabolic equations, initial value problems
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