In this paper we give an explicit formula for semigroups generated by 2$\times$2 operator matrices. Using this formula we can derive an estimate for the growth bound of the associated matrix generator. Finally these results are applied to a complete second order Cauchy problem yielding an explicit formula and a growth estimate for the solution of this problem.
Growth estimates for semigroups generated by 2x2 operator matrices
ENGEL, KLAUS JOCHEN OTTO
1991-01-01
Abstract
In this paper we give an explicit formula for semigroups generated by 2$\times$2 operator matrices. Using this formula we can derive an estimate for the growth bound of the associated matrix generator. Finally these results are applied to a complete second order Cauchy problem yielding an explicit formula and a growth estimate for the solution of this problem.File in questo prodotto:
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