A Neumann boundary value problem for a generalized Ginzburg–Landau equation

摘要

We study the following generalized 1D Ginzburg–Landau equation on Ω=(0,∞)×(0,∞):ut=(1+iμ)uxx+(a1+ib1)|u|2ux+(a2+ib2)u2ūx−(1+iν)|u|4u with initial and Neumann boundary conditions u(x,0)=h(x),ux(0,t)=P(t). Under suitable conditions, we prove that there is a unique weak solution that exists for all time.