Blow-up results for evolution problems with inhomogeneous nonlocal diffusion

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• 作者：Yujuan Chen^a ; Yueping Zhu^b ; ^{zhuyueping@ntu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Nonlocal diffusion ; Local existence ; Inhomogeneous ; Blow-up
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 December 2016
• 年：2016
• 卷：444
• 期：1
• 页码：452-463
• 全文大小：349 K

文摘

We provide a sufficient condition on the existence and nonexistence of global positive solutions to the Cauchy problem for an inhomogeneous nonlocal diffusion u_t=J⁎u−u+u^p+f(x)$u_t=J⁎u-u+u^p+f(x)$, where J   is a nonnegative function, p>0$p>0$, and f≥0,≢0$f\ge 0,\not\equiv 0$. Meanwhile, the case of an inhomogeneous nonlocal diffusion system is considered. It turns out that the inhomogeneous terms substantially contribute to the blow-up exponent, which coincides with the classical one when the diffusion is given by the Laplacian.