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- W1848048724 abstract "This paper is concerned with a type of nonlinear reaction–diffusion equation, which arises from the population dynamics. The equation includes a certain type reaction term u α ( 1 − σ ∫ R n u β d x ) of dimension n ≥ 1 and σ > 0 . An energy-methods-based proof on the existence of global solutions is presented and the qualitative behavior of solution which is decided by the choice of α , β is exhibited. More precisely, for 1 ≤ α < 1 + ( 1 − 2 / p ) β , where p is the exponent appears in Sobolev's embedding theorem defined in (3) , the equation admits global solution for any nonnegative initial data. Especially, in the case of n ≥ 2 and β = 1 , the exponent α < 1 + 2 / n is exactly the well-known Fujita exponent. The global existence result obtained in this paper shows that by switching on the nonlocal effect, i.e., from σ = 0 to σ > 0 , the solution's behavior differs distinctly, that's, from finite time blow-up to global existence." @default.
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- W1848048724 date "2016-12-01" @default.
- W1848048724 modified "2023-10-06" @default.
- W1848048724 title "A nonlocal reaction diffusion equation and its relation with Fujita exponent" @default.
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- W1848048724 doi "https://doi.org/10.1016/j.jmaa.2016.07.014" @default.
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