Global Asymptotical Behavior of Solutions to a Mixed Pseudo-Parabolic r (x)-Laplacian Equation

Jiazhuo Cheng ^[1] ; Shaomei Fang ^[2] ; Qiru Wang ^[1]
1. [1] Sun Yat-sen University
  
  Sun Yat-sen University
  
  China
2. [2] South China Agricultural University
  
  South China Agricultural University
  
  China
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 1, 2025
Idioma: inglés
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Resumen
- This paper concerns the asymptotic behavior of global solutions to the initial-boundary value problem of a mixed pseudo-parabolic r (x)-Laplacian equation. By employing the potential well method and Lagrange multiplier method, we prove the existence of ground state solutions for the stationary problem. Then by applying the Sobolev imbedding inequality and the Holder inequality, we establish a convergence rela- ¨ tionship between the global solutions of the evolution problem and the ground state solutions of the corresponding stationary problem.