A Stochastic Generalized Ginzburg-Landau Equation Driven by Jump Noise

TL;DR

This paper establishes the existence and uniqueness of solutions for a stochastic generalized Ginzburg-Landau equation driven by jump noise, using advanced analytical techniques to handle nonlinearities and stochastic effects.

Contribution

It introduces a novel approach to prove well-posedness for a complex stochastic PDE with jump noise and nonlinearities that do not satisfy standard monotonicity conditions.

Findings

Proved existence and uniqueness of solutions.

Developed a new analytical method for nonlinear stochastic PDEs.

Handled jump noise in the context of Ginzburg-Landau equations.

Abstract

This paper is concerned with the stochastic generalized Ginzburg-Landau equation driven by a multiplicative noise of jump type. By a prior estimate, weak convergence and monotonicity technique, we prove the existence and uniqueness of the solution of an initial-boundary value problem with homogeneous Dirichlet boundary condition. However, for the generalized Ginzburg-Landau equation, such a locally monotonic condition of the nonlinear term can not be satisfied in a straight way. For this, we utilize the characteristic structure of nonlinear term and refined analysis to overcome this gap.