Faedo-Galerkin Approximations for the nonlinear Deterministic Constrained Modified Swift-Hohenberg Equation

In this paper, we study the well-posedness of the nonlinear deterministic constrained modified Swift-Hohenberg equation; this equation belongs to class of amplitude equations which describe the appearance of pattern formation in nature. The proof for existence and uniqueness is based on the Faedo-Galerkin compactness method.