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Vortex annihilation in nonlinear heat flow for Ginzburg–Landau systems

Published online by Cambridge University Press:  26 September 2008

Patricia Bauman ,
Chao-Nien Chen ,
Daniel Phillips  and
Peter Sternberg
Patricia Bauman
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
Chao-Nien Chen
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN 47405, USA
Daniel Phillips
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
Peter Sternberg
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN 47405, USA
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Abstract

We consider the Cauchy problem for the system

where . Let e ∈ ℝ2 with |e| = 1. If u(x, 0) is smooth, bounded and

we prove u → e uniformly in x as t → ∞. Of particular interest is the motion of the zeros (vortices) of u. In this case, all zeros disappear after a finite time.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 6 , Issue 2 , April 1995 , pp. 115 - 126
Copyright
Copyright © Cambridge University Press 1995

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References

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