| 摘要: |
| 考虑带状区域中具有非均匀无界边界条件的一类拟线性抛物方程．在一定条件下，证明当时间t→∞时，初边值问题的解u趋于无穷．而且，利用零点性质还证明了：对任何x≠0，都有ux(x,t)→∞，即梯度也是渐近无界的． |
| 关键词: 曲率流 拟线性抛物方程 行波解 渐近行为 |
| DOI：10.20192/j.cnki.JSHNU(NS).2024.06.002 |
| 分类号:O175 |
| 基金项目: |
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| Asymptotic behavior of solutions of a parabolic equations in a band domain |
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DU Wenjing, HUANG Xinyu, WU Junyan, XIU Xinxiu, YUAN Lixia
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Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China
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| Abstract: |
| We consider a quasilinear parabolic equation in a band domain with inhomogeneous and unbounded boundary conditions. We show that, under certain conditions, the solution u of the initialboundary value problem tends to infinite as t→∞. Moreover, by using the zero number argument we show that for any x≠0, ux(x, t) also tends as t→∞ to infinity, that is, the gradient is asymptotically unbounded. |
| Key words: curvature flow quasilinear parabolic equation translating solution asymptotic behavior |
