On complete second order linear differential equations in Banach spaces (Q1114067)

The authors deal with the equation \(u''(t)+Bu'(t)+Au(t)=0\) \((t\geq 0)\) in a Banach space \(E\) where \(A, B\) are densely defined closed linear operators. Their main results are two necessary and sufficient conditions on \(A\), \(B\) for strong well posedness of the Cauchy problem. Moreover, they give explicit expressions for the propagators C(.), S(.), generalize some results in the case D(A)\(\supseteq D(B)\), and exhibit a partial differential equation.