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Double layered solutions to the extended Fisher–Kolmogorov P.D.E.
Nonlinear Differential Equations and Applications (NoDEA) ( IF 1.2 ) Pub Date : 2021-06-22 , DOI: 10.1007/s00030-021-00708-5 Panayotis Smyrnelis
中文翻译:
扩展的 Fisher-Kolmogorov PDE 的双层解
更新日期:2021-06-22
Nonlinear Differential Equations and Applications (NoDEA) ( IF 1.2 ) Pub Date : 2021-06-22 , DOI: 10.1007/s00030-021-00708-5 Panayotis Smyrnelis
We construct double layered solutions to the extended Fisher–Kolmogorov P.D.E., under the assumption that the set of minimal heteroclinics of the corresponding O.D.E. satisfies a separation condition. The aim of our work is to provide for the extended Fisher–Kolmogorov equation, the first examples of two-dimensional minimal solutions, since these solutions play a crucial role in phase transition models, and are closely related to the De Giorgi conjecture.
中文翻译:
扩展的 Fisher-Kolmogorov PDE 的双层解
我们构建了扩展的 Fisher-Kolmogorov PDE 的双层解,假设相应 ODE 的最小异宿组满足分离条件。我们工作的目的是提供扩展的 Fisher-Kolmogorov 方程,这是二维最小解的第一个例子,因为这些解在相变模型中起着至关重要的作用,并且与 De Giorgi 猜想密切相关。