杨丽丽,李中平.带有局部源的非局部扩散方程组的Fujita现象[J].数学研究及应用,2019,39(2):171~180 |
带有局部源的非局部扩散方程组的Fujita现象 |
Fujita-type Phenomenon of the Nonlocal Diffusion Equations with Localized Source |
投稿时间:2018-05-11 修订日期:2018-08-12 |
DOI:10.3770/j.issn:2095-2651.2019.02.006 |
中文关键词: 非局部扩散系统 Fujita临界曲线 第二临界曲线 全局存在 爆破 |
英文关键词:nonlocal diffusion system Fujita critical curve secondary critical curve global existence blow-up |
基金项目:国家自然科学基金(Grant No.11301419), 西华师范大学英才基金(Grant No.17YC382). |
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中文摘要: |
本文研究了一类带有局部源的非局部扩散系统$u_t=J*u-u+a(x)v^{p}$, $v_t=J*v-v+a(x)u^q$的柯西问题,首先根据是否存在全局解建立了Fujita曲线$(pq)_c=1+\max \{p+1,q+1\}$,也即证明了:如果$1(pq)_c$时,则既存在全局解,也存在非全局解.然后我还根据初始值在无穷远处的衰减率建立了第二临界曲线. |
英文摘要: |
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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