## Applications of semigroups of operators to non-elliptic differential operators.(English)Zbl 1064.47504

Summary: This paper treats systematically the semigroup method of non-elliptic differential operators, which was developed in the last ten years. In particular, a review of the applications of regularized semigroups to non-elliptic differential operators with constant coefficients or time-dependent coefficients, parabolic systems, correct systems, abstract differential operators and pseudodifferential operators is given here. It is also shown that the regularized semigroup is an appropriate tool for non-elliptic differential operators and is far superior to the integrated semigroup approach.

### MSC:

 47D60 $$C$$-semigroups, regularized semigroups 47D62 Integrated semigroups 47F05 General theory of partial differential operators 35P99 Spectral theory and eigenvalue problems for partial differential equations 47-02 Research exposition (monographs, survey articles) pertaining to operator theory 47N20 Applications of operator theory to differential and integral equations
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