Abstract
This paper concerns the asymptotic behavior of solutions to the homogeneous Neumann exterior problems of a class of semilinear parabolic equations with convection and reaction terms. The critical Fujita exponents theorems are established. It is shown that the global existence and blow-up of solutions depends on the reaction term, the convection term and the spatial dimension.
Highlights
In this paper, we consider the asymptotic behavior of solutions to the following problem: ∂u = ∂t u + λ x |x| · ∇u|x|λ tλ up, x ∈ Rn \ B, t >, ( ) ∂u =,∂ν x ∈ ∂B, t >, u(x, ) = u (x), x ∈ Rn \ B, where λ, λ, λ ≥, p >, ≤ u ∈ C(Rn \ B ) ∩ L∞(Rn \ B ), B is the unit ball in Rn
1 Introduction In this paper, we consider the asymptotic behavior of solutions to the following problem:
To prove the blow-up of solutions, we will determine the interactions among the diffusion terms, convection terms and reaction terms by a series of precise integral estimates instead of pointwise comparisons
Summary
Introduction In this paper, we consider the asymptotic behavior of solutions to the following problem: Where λ , λ , λ ≥ , p > , ≤ u ∈ C(Rn \ B ) ∩ L∞(Rn \ B ), B is the unit ball in Rn. The studies on asymptotic behavior of solutions to diffusion equations with nonlinear reaction was begun in by Fujita in [ ], where it was proved that for the Cauchy problem to the semilinear equation We call pc the critical Fujita exponent and such a result a blow-up theorem of Fujita type.
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