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The Ginzburg-Landau Equation: Posed in a Quarter-Plane

✍ Scribed by C. Bu

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
685 KB
Volume
176
Category
Article
ISSN
0022-247X

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✦ Synopsis

We study the following Ginzburg-Landau equation (GL): (u_{t}=(v+i x) u_{x x}-) ((\kappa+i \beta)|u|^{2} u+\gamma u, v>0, \kappa>0, \alpha \neq 0). For a full-line problem with (u(x, 0)=) (u_{0}(x) \in H^{2}(-\infty, x)), global existence-uniqueness is established. For a half-line problem with (u(x, 0)=u_{0}(x) \in H^{2}[0, \infty), u(0, t)=Q(t) \in C^{2}[0, \infty), u_{0}(0)=Q(0)), the following results are available: (1) local existence-uniqueness; (2) criteria for the existence of a small amplitude solution on any finite interval by means of small initial and boundary data; (3) global existence in the case (|\beta| \leqslant \sqrt{3} \kappa) or (\alpha \beta>0). i. 1993 Academic Press. Inc

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