A Cauchy problem of spatial-weighted reaction–diffusion equations. (June 2019)

• Record Type: Journal Article
• Authors: Liu, Bingchen; Lin, Hongyan
• Is Part Of: Applied mathematics letters. Volume 92(2019)
• Page Start: 128
• Page End: 133
• Publication Date: 2019-06
• Subjects: Cauchy problem -- Fujita exponent -- Spatial-weighted function; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2019.01.021
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: This paper deals with a Cauchy problem of reaction–diffusion equations u t = Δ u + b ( x ) u α v p and v t = Δ v + a ( x ) u q v β in R N × [ 0, T ) with p, q, α, β ≥ 0 . The weighted functions a ( x ), b ( x ) are locally Hölder-continuous, satisfying that a ( x ) ∼ | x | m and b ( x ) ∼ | x | n as | x | → + ∞ for m, n ≥ 0 . The complete classification on global and non-global solutions is obtained through determining the Fujita exponent which is affected by m, n, p, q, α, β, N . The results of the paper extend the ones obtained by Escobedo and Herrero (1991) and Li, Sun and Zhang (2017), respectively, to the completely coupled equations.