English

Some dynamical properties of constrained Modified Swift-Hohenberg Equation

Analysis of PDEs 2025-05-08 v1 Dynamical Systems

Abstract

In this paper, we have studied the long-term behavior for the projected deterministic constrained modified Swift-Hohenberg equation with constraints and Dirichlet boundary conditions. Specifically, using Lojasiewicz-Simon inequality, we have shown that the global solution approaches an equilibrium state. Also, we have analyzed the rate at which the solution approaches equilibrium. Finally, we have proven the existence of a global attractor.

Keywords

Cite

@article{arxiv.2505.04194,
  title  = {Some dynamical properties of constrained Modified Swift-Hohenberg Equation},
  author = {Saeed Ahmed and Javed Hussain},
  journal= {arXiv preprint arXiv:2505.04194},
  year   = {2025}
}