IJPAM: Volume 23, No. 1 (2005)

NON-HOMOGENEOUS QUASI-LINEAR SYMMETRIC
HYPERBOLIC SYSTEMS WITH
CHARACTERISTIC BOUNDARY

Paolo Secchi$^1$, Paola Trebeschi$^2$
$^{1,2}$Department of Mathematics
Faculty of Engineering
University of Brescia
Via Valotti 9, Brescia, 25133, ITALY
$^1$email: secchi@ing.unibs.it
$^2$email: paola.trebesc@ing.unibs.it


Abstract.We consider the initial-boundary value problem for quasi-linear symmetric hyperbolic systems with characteristic boundary of constant multiplicity. We show the existence of regular solutions in suitable functions spaces which take into account the loss of regularity in the normal direction to the characteristic boundary. The paper extends known results for problems with homogeneous boundary conditions to the nonhomogeneous case, under conditions of sharp regularity for the boundary data.

Received: June 1, 2005

AMS Subject Classification: 35L40, 35L50, 35L45

Key Words and Phrases: initial boundary value problem, characteristic boundary, symmetric hyperbolic systems

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 23
Issue: 1