The introduction of the Landau–Ginzburg free energy provides a framework to generalize the diffusion beyond the classical fickian approach. The analysis shows the existence and uniqueness of solutions with a priori bounds and making use of the Fixed Point Theorem to a suitable abstract evolution. Asymptotic solutions are provided with the Hamilton–Jacobi operator and a positivity condition is formulated based on an asymptotic positive kernel. Further, the positive region is characterized and a precise assessment is provided. Afterwards, the problem is analyzed in the Travelling Waves domain to show the phenomena of waves synchronization and to provide linear manifolds in the proximity of the critical points. Finally, numerical TW profiles are obtained and the amplitude of a positive region in the TW domain is provided as a function of the TW‑speed.

中文翻译：

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具有高阶扩散算子的入侵物种动力学

Landau-Ginzburg 自由能的引入提供了一个框架来概括经典菲克方法之外的扩散。分析显示了具有先验界限的解的存在性和唯一性，并利用不动点定理进行了适当的抽象演化。使用 Hamilton-Jacobi 算子提供渐近解，并基于渐近正核制定正条件。此外，表征阳性区域并提供精确的评估。然后，在行波域中分析该问题以显示波同步现象并在关键点附近提供线性流形。最后，获得数值 TW 剖面，并提供 TW 域中正区域的幅度作为 TW 速度的函数。