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

作者：Matsumoto Toshitaka^*; Tanaka Naoki

来源：Journal of Approximation Theory, 2011, 163(9): 1217-1237.

DOI：10.1016/j.jat.2011.04.002

• Product formula
• Semigroup of Lipschitz operators
• Semilinear evolution equation of parabolic type
• Analytic semigroup
• Fractional power
• Fractional step method

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.

• 出版日期2011-9