Studies on well-posedness for semilinear evolution equations with constraints and their applications

半线性演化方程的算子和适定性。我们在拟收缩半群的生成上推广了先前的结果，并应用所得结果证明了复Ginzburg-Landau方程、漂移-扩散方程、二维Navier-Stokes方程和强退化抛物方程的适定性。得到了Lipschitz算子半群的一个收敛定理、一个近似定理和Chernoff型的乘积公式。

operators and well-posedness for semilinear evolution equations. We extended the former results on the generation of quasi-contractive semigroups and applied the obtained results to show the well-posedness of the complex Ginzburg-Landau equation, drift-diffusion equations, 2-dimensional Navier-Stokes equation and strongly degenerate parabolic equations. We also obtained a convergence theorem, an approximation theorem and product formulas of Chernoff type for semigroups of Lipschitz operators.