论文标题
大型不均匀性可以产生目标模式吗？
Can large inhomogeneities generate target patterns?
论文作者
论文摘要
我们研究了局部耦合弱且存在杂质或缺陷的振荡介质中目标模式的存在。我们使用在平面上构成的粘性Eikonal方程对这些系统进行建模，并将缺陷表示为扰动。与以前的结果相反，我们考虑了大缺陷，我们使用具有缓慢代数衰减的功能来描述，即$ g \ sim {\ sim {\ Mathcal o}（1/| x |^m）$ for $ m \ in（1,2] $。我们证明，这些缺陷能够生成较小的目标，以及较小的参数，以及较小的范围，以及较小的局部范围，均具有较小的范围，并且均具有较小的范围，并且该频率是均等的。描述它们的强度。系统选择的模式。
We study the existence of target patterns in oscillatory media with weak local coupling and in the presence of an impurity, or defect. We model these systems using a viscous eikonal equation posed on the plane, and represent the defect as a perturbation. In contrast to previous results we consider large defects, which we describe using a function with slow algebraic decay, i.e., $g \sim {\mathcal O}(1/|x|^m)$ for $m \in (1,2]$. We prove that these defects are able to generate target patterns and that, just as in the case of strongly localized impurities, their frequency is small beyond all orders of the small parameter describing their strength. Our analysis consists of finding two approximations to target pattern solutions, one which is valid at intermediate scales and a second one which is valid in the far field. This is done using weighted Sobolev spaces, which allow us to recover Fredholm properties of the relevant linear operators, as well as the implicit function theorem, which is then used to prove existence. By matching the intermediate and far field approximations we then determine the frequency of the pattern that is selected by the system.
