Fujita-type Phenomenon of the Nonlocal Diffusion Equations with Localized Source
Received:May 11, 2018  Revised:August 12, 2018
Key Word: nonlocal diffusion system   Fujita critical curve   secondary critical curve   global existence   blow-up  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11301419) and the Meritocracy Research Funds of China West Normal University (Grant No.17YC382).
Author NameAffiliation
Lili YANG College of Mathematics and Information, China West Normal University, Sichuan 637000, P. R. China 
Zhongping LI College of Mathematics and Information, China West Normal University, Sichuan 637000, P. R. China 
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Abstract:
      In this paper, we investigate the Cauchy problem for the nonlocal diffusion system with localized source $u_t=J*u-u+a(x)v^{p}$, $v_t=J*v-v+a(x)u^q$. We first prove that the Fujita curve is $(pq)_c=1+\max \{p+1,q+1\}$ based on whether there exist global solutions, that is, if $1(pq)_c$, there exist both global and non-global solutions to the problem. Furthermore, we establish the secondary critical curve on the space-decay of initial value at infinity.
Citation:
DOI:10.3770/j.issn:2095-2651.2019.02.006
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