IJPAM: Volume 56, No. 4 (2009)

ON HYPERBOLIC SECOND-ORDER QUASI-LINEAR
INITIAL BOUNDARY-VALUE PROBLEMS

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


Abstract.The paper deals with the existence and uniqueness of a non-trivial classical solution to a initial boundary-value problem for a quasi-linear second-order system, with homogeneous boundary conditions, in the space $H^{s'}(\bar{\Omega}\times[0,T])$, where $\Omega$ is the half-space $\Omega = {\mathbf R}^{d-1} \times (0,\infty)$, $s > d/2 +3$ and $s'\in (0,s)$. The proof of the main theorem relies on the existence of the solution in $H^{s}(\bar{\Omega}\times[0,T])$, to the boundary-value problem, for linear second-order systems with smooth coefficients in the variables $x$ and $t$. The main result is achieved by defining a suitable iteration scheme that approximates the solution.

Received: September 23, 2009

AMS Subject Classification: 35L55

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

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 56
Issue: 4