Shibata, Yoshihiro On the Neumann problem for some linear hyperbolic systems of second order. (English) Zbl 0674.35056 Tsukuba J. Math. 12, No. 1, 149-209 (1988). A unique existence theorem of solutions to the mixed problem for linear hyperbolic systems of second order with generalized inhomogeneous Neumann boundary condition is obtained. The coefficients in the system is only required to be in the space \({\mathcal B}^ 2\), and it is shown that the constants appearing in the first energy inequality depend essentially only on \({\mathcal B}^{1+\mu}\)-norms \((0<\mu \ll 1)\) of coefficients of the operator. Reviewer: S.Chen Cited in 8 Documents MSC: 35L55 Higher-order hyperbolic systems 35L20 Initial-boundary value problems for second-order hyperbolic equations 35B45 A priori estimates in context of PDEs 35A05 General existence and uniqueness theorems (PDE) (MSC2000) Keywords:energy method; unique; existence; mixed problem; Neumann boundary condition; first energy inequality PDFBibTeX XMLCite \textit{Y. Shibata}, Tsukuba J. Math. 12, No. 1, 149--209 (1988; Zbl 0674.35056) Full Text: DOI