Blow-up analyses in reaction–diffusion equations with Fujita exponents

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Fengjie Li, Hongyan Lin, Bingchen LiuAbstractIn this paper, we study the reaction–diffusion equations with variable coefficients in some bounded domains. At least one of the components of solutions blows up for every initial data in some exponent regions, where the Fujita exponents are determined by the exponents of the sources and the coefficients and the dimension of the domain. We also show the classifications of simultaneous and nonsimultaneous blow-up of the components of solutions. The asymptotic properties are discussed including blow-up rates and sets. Moreover, the upper and the lower bounds of blow-up time are given for all dimensions of domains, respectively.

Source: Nonlinear Analysis: Real World Applications - May 31, 2019 Category: Research Source Type: research