  We study the Cauchy problem for the half Ginzburg-Landau-Kuramoto (hGLK)
equation with the second order elliptic operator having rough coefficients and
potential type perturbation. The blow-up of solutions for hGLK equation with
non-positive nonlinearity is shown by an ODE argument. The key tools in the
proof are appropriate commutator estimates and the essential self-adjointness
of the symmetric uniformly elliptic operator with rough metric and potential
type perturbation.
