| 摘要: |
| 我们考虑一类带有Dirichlet边界条件的正的双稳定型退化反应扩散方程解的渐近行为．我们首先证明了一个收敛性结果．进一步，通过引入一组非负有紧支集的初值函数，证明了该问题解的渐近行为的小传播-大传播二分性结果． |
| 关键词: 渗流方程 Dirichlet边界条件 渐近行为 |
| DOI：10.20192/j.cnki.JSHNU(NS).2024.06.001 |
| 分类号:O175.2 |
| 基金项目: |
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| Convergence of solutions to the degenerate reaction diffusion equation with Dirichlet boundary condition |
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LI Fang, LI Xin, XIAHOU Zhen, XIE Jiangting
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Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China
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| Abstract: |
| We consider the asymptotic behavior of solutions to the porous medium equation with a positive bistable type reaction term and Dirichlet boundary condition. We first prove a convergence result. Furthermore, by investigating families of initial data of the type {Øσ}σ＞0, where Øσ belongs to an appropriate class of nonnegative compactly supported functions, we prove small spreading-big spreading dichotomy on the asymptotic behavior of the solutions. |
| Key words: porous medium equation Dirichlet boundary condition asymptotic behavior |
