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

2024/11/06 by Ahmed, Saeed, Hussain, Javed · 2 citations
#35K61 #35R01 #47J35 #58J35 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.03858

Abstract

In this paper, we are interested in proving the existence and uniqueness of the local, local maximal, and global solutions of the equation projected on the Hilbert manifold. Furthermore, we show that, for any given initial data in the Hilbert manifold M, the solution to this equation is also in the Hilbert manifold M. Finally, we demonstrate that the solution to the equation is a gradient flow.

Cited by

• Some dynamical properties of constrained Modified Swift-Hohenberg Equation
• Martingale Solutions of Stochastic Constrained Modified Swift-Hohenberg Equation

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