Some dynamical properties of constrained Modified Swift-Hohenberg Equation

2025/05/07 by Saeed Ahmed, Ahmed, Saeed, Javed Hussain +1
Engineering · #335R01 #35K61 #47J35 #58J35 #Analysis of PDEs (math.AP) #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Stability and Controllability of Differential Equations #Thermoelastic and Magnetoelastic Phenomena

paper · pdf · doi:10.48550/arxiv.2505.04194

openalex publication_date 2025/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On the Global Solution and Invariance of nonlinear Constrained Modified Swift-Hohenberg Equation on Hilbert Manifold

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