Global solutions for initial-boundary value problem of quasilinear wave equations (Q931650)

An IBV problem for a class of quasilinear wave equations is considered. The equation is transformed into a system of differential-integral equations and further into an equivalent hyperbolic system of balance laws. For the IBV Riemann problem one shows the existence of solution near the boundary layer by using the contraction mapping principle. Approximate solutions of the IBV problem are obtained by applying the generalized Glimm's scheme. Under certain conditions regarding the coefficients of the equation, the existence of global Lipschitz continuous solutions is proved. This is done by means of establishing the global existence for the derivatives of solutions and the weak convergence of residuals for the approximate solutions.