IJPAM: Volume 49, No. 1 (2008)

SECOND-ORDER QUASI-LINEAR
BOUNDARY-VALUE PROBLEMS

Rita Cavazzoni
via Millaures 12, Torino, 10146, ITALY
e-mail: cavazzon@interfree.it


Abstract.We discuss the well-posedness of quasi-linear hyperbolic second-order boundary-value problems in the half-space $\Omega = \frak{R}^{d-1} \times (0,\infty)$, with homogeneous boundary conditions. At first, we consider second-order boundary-value problems for linear systems having smooth coefficients, that depend on the space-variable and on the time-variable. We prove the well-posedness in the space $C^1([0,T], H^{s-2}(\Omega)^d)$, with $s\in \frak{R}$. Next, by applying the previous result, we study quasi-linear boundary-value problems and establish the existence of a non-null solution in $C([0,T], H^{s'}(\Omega)^d)$ with $s'\in (0,s)$ and $s > d/2 +2$. The main result is proved by approximating the solution through an iteration scheme.

Received: September 10, 2008

AMS Subject Classification: 35L55

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

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 49
Issue: 1