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.