Dirichlet inhomogeneous boundary value problem for the n+1 complex Ginzburg-Landau equation |
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Authors: | Hongjun Gao Charles Bu |
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Affiliation: | a Department of Mathematics, Nanjing Normal University, Nanjing 210097, China b Department of Mathematics, Wellesley College, Wellesley, MA 02481, USA |
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Abstract: | We study the following complex Ginzburg-Landau equation with cubic nonlinearity on for under initial and Dirichlet boundary conditions u(x,0)=h(x) for x∈Ω, u(x,t)=Q(x,t) on ∂Ω where h,Q are given smooth functions. Under suitable conditions, we prove the existence of a global solution in H1. Further, this solution approaches to the solution of the NLS limit under identical initial and boundary data as a,b→0+. |
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Keywords: | 35K55 35R35 35K50 |
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