A remark on global bifurcations of solutions of Ginzburg-Landau equation

作者：Hirano Norimichi; Rybicki Slawomir^*

来源：Nonlinear Analysis: Real World Applications , 2011, 12(6): 2943-2946.

DOI：10.1016/j.nonrwa.2011.04.006

• Ginzburg-Landau equation
• Global bifurcation

We have proved that all the closed connected sets of solutions of the complex Ginzburg-Landau equation
{-Delta u(x) + 2i < A(x), del u(x)> + parallel to A(x)parallel to(2)u(x) = lambda(1 - vertical bar u(x)vertical bar(2))u(x) in Omega,
u = 0 on partial derivative Omega.
bifurcating from the set of normal solutions {0} x (0, + infinity) subset of H-0(1) (Omega, C) x (0, + infinity) are unbounded, where Omega subset of R-2 is an open, bounded domain with smooth boundary, A(x(1), x(2)) = (-x(2), x(1)) and parallel to . parallel to is the usual norm in R-2.

• 出版日期2011-12