带状区域中一类抛物方程解的渐近行为
Asymptotic behavior of solutions of a parabolic equations in a band domain
杜文静 1黄鑫宇 1吴俊彦 1修新秀 1袁丽霞1
作者信息
- 1. 上海师范大学数理学院,上海 200234
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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.
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 initial-boundary 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.
关键词
曲率流/拟线性抛物方程/行波解/渐近行为Key words
curvature flow/quasilinear parabolic equation/translating solution/asymptotic behavior引用本文复制引用
出版年
2024
NETL
NSTL
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