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

算子与半线性发展方程的适定性。我们推广了前人关于拟压缩半群生成的结果，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Chernoff型收敛定理、逼近定理和乘积公式。

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.