Abstract.We consider linear evolution boundary-value problems for third-order systems in a half-space of , with Neumann-type homogeneous boundary conditions, both with constant and variable coefficients. As far as the constant coefficient case is concerned, by performing a Fourier-Laplace transform, we discuss the well-posedness of the problem in the Sobolev space , proving a necessary condition (Lopatinskii condition) and a sufficient condition. This last statement is established through the application of Hille-Yosida Theorem. In the case where the system has variable coefficients, we focus on the well-posedness of the boundary-value problem in a half-space, by means of Hille-Yosida result again.

Received: August 20, 2007

AMS Subject Classification: 35L55

Key Words and Phrases: initial boundary-value problem, Lopatinskii condition, third-order systems

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 43
Issue: 1