@Article{JPDE-33-3,
author = {Jiahui, Huang and Yuan, Junli and Zhao, Yan},
title = {Blowup and Asymptotic Behavior of a Free Boundary Problem with a Nonlinear Memory},
journal = {Journal of Partial Differential Equations},
year = {2020},
volume = {33},
number = {3},
pages = {249--260},
abstract = {<p style="text-align: justify;">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 $T^*&lt;+\infty$, 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.</p>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v33.n3.5},
url = {https://global-sci.com/article/88164/blowup-and-asymptotic-behavior-of-a-free-boundary-problem-with-a-nonlinear-memory}
}