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Global existence for the generalised 2D Ginzburg-Landau equation

Published online by Cambridge University Press:  17 February 2009

Hongjun Gao  and
Keng-Huat Kwek
Hongjun Gao
Affiliation:
Department of Mathematics, Nanjing Normal University, Nanjing 210097, P. R. China; e-mail: [email protected].
Keng-Huat Kwek
Affiliation:
Department of Mathematics, The National University of Singapore, 10 Kent Ridge Crescent, Singapore119260.
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Abstract

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Ginzburg-Landau type complex partial differential equations are simplified mathematical models for various pattern formation systems in mechanics, physics and chemistry. Most work so far has concentrated on Ginzburg-Landau type equations with one spatial variable (1D). In this paper, the authors study a complex generalised Ginzburg-Landau equation with two spatial variables (2D) and fifth-order and cubic terms containing derivatives. Based on detail analysis, sufficient conditions for the existence and uniqueness of global solutions are obtained.

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 3 , January 2003 , pp. 381 - 392
Copyright
Copyright © Australian Mathematical Society 2003

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