Fast diffusion in a porous building material with a nonlocal source
作者：
Highlights：
• The paper deals with a fast diffusion equation in the whole space with a nonlocal term. We motivate the problem by pointing out such equations are important in processes demanding fast solidification, for instance, on repairs in an urgent accident or in submarine engineering.
• The aim of the paper is to provide the critical Fujita exponent and the second critical exponent for problem (2.3). And we show the effect of weight function K(x) and coefficient q in nonlocal term on the evolution of solutions. We find that the large s (i.e. small K(x)) or the large q is beneficial to the global existence of solutions.
摘要
•The paper deals with a fast diffusion equation in the whole space with a nonlocal term. We motivate the problem by pointing out such equations are important in processes demanding fast solidification, for instance, on repairs in an urgent accident or in submarine engineering.•The aim of the paper is to provide the critical Fujita exponent and the second critical exponent for problem (2.3). And we show the effect of weight function K(x) and coefficient q in nonlocal term on the evolution of solutions. We find that the large s (i.e. small K(x)) or the large q is beneficial to the global existence of solutions.
论文关键词：Fast diffusion,Critical exponent,Global existence,Blow-up,Fractal calculus,Fast solidification,Fast diffusion law,Catastrophe
论文评审过程：Received 2 August 2019, Revised 5 April 2020, Accepted 19 April 2020, Available online 7 May 2020, Version of Record 7 May 2020.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125327
