Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 48, pp. 1-16.

Title: Existence and stability of forced waves for p-Laplace equations in a shifting habitat

Authors: Tianyuan Xu (Guangdong Univ. of Technology, Guangzhou, China)
         Gege Liu (South China Normal Univ., Guangzhou, Guangzhou, China)
         Jingxue Yin (South China Normal Univ., Guangzhou, Guangdong, China)

Abstract:
This article concerns the existence and stability of forced waves for 
p-Laplace equations with a shifting habitat given by a non-decreasing function 
with a sign change.
The existence of forced waves is studied by the monotone iteration 
method combined with a pair of delicate super- and sub-solutions.
Finally, we develop an approximating weighted energy method to prove 
the $L^p$ stability and exponential convergence of forced waves.

Submitted December 1, 2024. Published May 08, 2025.
Math Subject Classifications: 35K65, 35K57, 35C07, 92D25.
Key Words: Forced waves; p-Laplacian diffusion; shifting habitats; stability.