Strongly damped wave equations with fractional diffusions: well-posedness and global attractors
Abstract
This paper is concerned with the nonlinear strongly damped wave equations involving the fractional Laplacian and regional fractional Laplacian with various boundary conditions. We first prove the existence and uniqueness of weak solutions using the compactness method and weak convergence techniques in Orlicz spaces. Then we study the existence and regularity of global attractors of associated semigroups. The main novelty of the obtained results here is to improve and extend the previous results in [6, 7, A.N. Carvalho and J.W. Cholewa] and [24, J. Shomberg].
Fields of Study & Subjects
Stability and Controllability of Differential Equations
Nonlinear Differential Equations Analysis
Fractional Differential Equations Solutions
Publication details
- Journal / source
- Advances in Pure and Applied Mathematics
- Volume
- 17
- Issue
- 1
- Pages
- 1–24
- Publication date
- 1 January 2026
- Language
- FR