Time-periodic boundary layer solutions to singularly perturbed parabolic problems
Time-periodic boundary layer solutions to singularly perturbed parabolic problems
复制标题
DOI：
10.1016/j.jde.2016.12.020
复制
发表时间：
2016-09
期刊：
影响因子：
--
通讯作者：
L. Recke;V. Butuzov;N. Nefedov
中科院分区：
文献类型：
--
作者：
L. Recke;V. Butuzov;N. Nefedov
在这篇文章中，我们给出了一个隐函数定理类型的结果，它是为应用于奇异摄动问题而设计的。这一结果是基于压缩映象的不动点迭代，特别地，不需要单调性或保号性质。然后，我们将我们的抽象结果应用于具有两个独立奇异摄动参数的半线性抛物问题的时间周期边界层解(允许关于空间变量非单调)。我们证明了这些解的存在性和局部唯一性，并估计了它们到某些近似解的距离。
In this paper, we present a result of implicit function theorem type, which was designed for applications to singularly perturbed problems. This result is based on fixed point iterations for contractive mappings, in particular, no monotonicity or sign preservation properties are needed. Then we apply our abstract result to time-periodic boundary layer solutions (which are allowed to be non-monotone with respect to the space variable) in semilinear parabolic problems with two independent singular perturbation parameters. We prove existence and local uniqueness of those solutions, and estimate their distance to certain approximate solutions.