\(L^p\)-maximal regularity for second order Cauchy problems (Q2575656)

The authors introduce the concept of \(L^p\)-maximal regularity for the abstract linear second order Cauchy problem \[ \ddot{u}(t)+B\dot{u}(t)+Au(t)=f(t), \;t\in [0,T), \quad u(0)=\dot u(0)=0, \] where \(u(t)\) takes its values in a Banach space \(X\); and \(A,B\) are closed linear operators on \(X\). They prove \(L^p\)-maximal regularity for an abstract model problem and apply the results obtained to nonlinear wave equations to establish existence, uniqueness of the solutions and their regularity properties.