ANZIAM  J.  44 (2003), 381-392
Global existence for the generalised 2D Ginzburg-Landau equation

Hongjun Gao
  Department of Mathematics
  Nanjing Normal University
  Nanjing 210097
  P. R. China
Keng-Huat Kwek
  Department of Mathematics
  The National University of Singapore
  10 Kent Ridge Crescent
  Singapore 119260

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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