Operator models in elasticity theory and hydromechanics and the associated analytic semigroups. (Q1596163)

The paper deals with the equations of the type of \(\,\ddot x + B\dot x + Ax = 0\), where \(A\) is positive self-conjugated operator and \(B\) is sectorial operator which are determined in the Hilbert space \({\mathcal H}\). The authors establish the conditions under which the linearizor \[ {\mathcal A}_B = \begin{pmatrix} 0 & I\\ -A & -B\end{pmatrix} \] generates the analytical \(C_0\)-semigroup in the energy space \(\,E = {\mathcal D}(A^{1/2})\times {\mathcal H}\). The semigroup analyticity is determined under some additional condi tions.