Nonlocal abstract ginzburg-landau type equations and application

Abstract

We study a nonlocal abstract Ginzburg–Landau type equation. The equation includes variable coefficients with convolution terms and an abstract linear operator function A in a Fourier-type Banach space E. For sufficiently smooth initial data, assuming growth conditions for the operator A and the coefficient a, the existence and uniqueness of the solution and the Lp -regularity properties are established. We obtain the existence and uniqueness of the solution, and the regularity of different classes of nonlocal Ginzburg–Landau-type equations by choosing the space E and operator A that occur in a wide variety of physical systems.