The generalized Ginzburg–Landau equation: posed in a quarter plane

摘要

This paper is concerned with a generalized 1D Ginzburg–Landau equation involving a fifth order term and two nonlinear terms containing spatial derivatives. The equation is posed in a quarter plane 0⩽x,t<∞ with initial condition and Robin inhomogeneous boundary condition. Existence of a unique global solution in H1 is shown under suitable conditions.