Abstract.We consider linear hyperbolic boundary-value problems for second-order systems in a half-space, both for operators with constant coefficients and for operators with coefficients which depend explicitly on the space-variable. Concerning the operator with constant coefficients, we prove, by means of the Fourier-Laplace analysis and the application of Hille-Yosida Theorem, that the problem with homogeneous boundary condition and divergence-free constraint is strongly well-posed in the Sobolev space . Furthermore, we prove that the problem admits finite energy surface waves. Next, we discuss the boundary-value problem for a linear second-order differential operator with variable coefficients. A sufficient condition for strong well-posedness is proved, by means of Hille-Yosida Theorem.

Received: December 7, 2007

AMS Subject Classification: 35L55

Key Words and Phrases: hyperbolic second-order system, boundary-value problem

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 43
Issue: 3