Year: 2020
Author: Jiahui Huang, Junli Yuan, Yan Zhao
Journal of Partial Differential Equations, Vol. 33 (2020), Iss. 3 : pp. 249–260
Abstract
In this paper, we investigate a reaction-diffusion equation $u_t-du_{xx}=au+\int_{0}^{t}u^p(x,\tau){\rm d}\tau+k(x)$ with double free boundaries. We study blowup phenomena in finite time and asymptotic behavior of time-global solutions. Our results show if $\int_{-h_0}^{h_0}k(x)\psi_1 {\rm d}x$ is large enough, then the blowup occurs. Meanwhile we also prove when $T^*<+\infty$, the solution must blow up in finite time. On the other hand, we prove that the solution decays at an exponential rate and the two free boundaries converge to a finite limit provided the initial datum is small sufficiently.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v33.n3.5
Journal of Partial Differential Equations, Vol. 33 (2020), Iss. 3 : pp. 249–260
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Nonlinear memory free boundary blowup asymptotic behavior.