A Dirichlet boundary value problem for a generalized Ginzburg-Landau equation

Abstract We study the following generalized 1D Ginzburg-Landau equation on Ω = (0,∞) × (0, ∞): u t = (1 + iμ)u xx + (a 1 + ib 1 )|u| 2 u x + (a 2 + ib 2 )u 2 u x − (1 + iν)|u| 4 u with initial and Dirichlet boundary conditions u(x,0) = h(x),u(0,t) = Q(t). Under suitable conditions, we prove that there is a unique H1 solution that exists for all time.

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