Fujita-type phenomenon of the nonlocal diffusion equations with localized source
Received:May 11, 2018  Revised:May 11, 2018
Key Word: Nonlocal diffusion system   Fujita critical curve   Secondary critical curve   Global existence   Blow-up  
Fund ProjectL:the National Science Foundation of China (11301419), and the Meritocracy Research Funds of China West Normal University (17YC382)
Author NameAffiliationE-mail
Lili Yang China West Normal University liliyang1213@126.com 
Zhongping Li China West Normal University zhongpingli80@126.com 
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      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.
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