| In this thesis, the problem of 2×2 operator matrices generating C0 semigroups is investi-gated, and some sufficient conditions for upper-triangular and skew-diagonal operator matrices to generate C0 semigroups are given.The results are applied to the operator matrices, for ex-ample, generated by two classes of mixed problem of parabolic equations. It is showed that these operator matrices generate semigroups, and that the correctness of the results are demon-strated by Hille-Yosida's theorem. Moreover, the expressions of semigroups generated by these operator matrices are presented.
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