Abstract

Consider the system Autt+Cuxx=f(x,t), (x,t)T for u(x,t) in 2, where A and C are real constant 2×2 matrices, and f is a continuous function in 2. We assume that detC0 and that the system is strictly hyperbolic in the sense that there are four distinct characteristic curves Γi, i=1,,4, in xt-plane whose gradients (ξ1i,ξ2i) satisfy det[Aξ1i2+Cξ1i2]=0. We allow the characteristics of the system to be given by dt/dx=±1 and dt/dx=±r, r(0,1). Under special conditions on the boundaries of the region T={(x,t)t1,(1+r+t)/rx(1+rt)/r}, we will show that the system has a unique C2 solution in T.