A systematization of the \(L^ 2\)-well-posed mixed problem and its applications to the mixed problem for weakly hyperbolic equations of second order. II (Q750745)

[For part I see Funkc. Ekvacioj, Ser. Int. 31, No.2, 249-296 (1988; Zbl 0686.35068).] The paper contains two main results: 1) one obtains a complete and applicable systematization of the \(L^ 2\)- well-posed mixed problem for regularly hyperbolic equations of second order with real boundary operators; 2) one proves that a certain mixed problem for the weakly hyperbolic equations of second order degenerating on the initial surface is \(C^{\infty}\)-well-posed. By means of the obtained systematization, the mixed problem is reduced to the problem with non-negative type boundary condition for symmetric hyperbolic pseudodifferential systems of first order. The \(C^{\infty}\)-well-posedness is obtained by using energy estimates.