Blowup and Asymptotic Behavior of a Free Boundary Problem with a Nonlinear Memory |
| |
| Authors: | Jiahui Huang Junli Yuan & Yan Zhao |
| |
| Affiliation: | School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China;School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China;School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China |
| |
| 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. |
| |
| Keywords: | Nonlinear memory free boundary blowup asymptotic behavior |
| 本文献已被 万方数据 等数据库收录！ |
| 点击此处可从《偏微分方程英文版》浏览原始摘要信息 |
|
