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Matano, H., Nara, M. and Taniguchi, M. (2009) Stability of Planar Waves in the Allen-Cahn Equation. Communications in Partial Differential Equations, 34, 976-1002.
https://doi.org/10.1080/03605300902963500

has been cited by the following article:

• TITLE: Stability of Traveling Wave Solutions for Degenerate Fisher Type Equations with Fractional Laplacian

  AUTHORS: Yahan Wang, Yunna Zhang, Huiqin Lu

  KEYWORDS: Lyapunov Stability, Asymptotic Behavior, Sub-Super Solution Method, Traveling Wave Solution, Fisher Type Equation

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.14 No.1, December 29, 2025

  ABSTRACT: In this paper, we study the Lyapunov stability of traveling wave solutions for degenerating Fisher type equations with fractional Laplacian. First, we give the asymptotic behavior of the derivative of the traveling wave solutions at negative infinity by using the maximum principle. Second, we construct the subsolution and supersolution of the initial value problem in a moving coordinate frame. Finally, we use the sub-super solution method to prove the Lyapunov stability of traveling wave solutions in the polynomially weighted space.