ANZIAM J.
44 (2003), 381-392
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Global existence for the generalised 2D Ginzburg-Landau equation
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Hongjun Gao
Department of Mathematics
Nanjing Normal University
Nanjing 210097
P. R. China
gaohj@pine.njnu.edu.cn
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Keng-Huat Kwek
Department of Mathematics
The National University of Singapore
10 Kent Ridge Crescent
Singapore 119260
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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.
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