A product formula for semigroups of Lipschitz operators associated with semilinear evolution equations of parabolic type

A product formula for semigroups of Lipschitz operators associated with semilinear evolution equations of parabolic type is discussed under a new type of stability condition which admits “error term”. The result obtained here is applied to showing the convergence of approximate solutions constructed by a fractional step method to the solution of the complex Ginzburg–Landau equation.