Nonhomogeneous quasilinear hyperbolic system arising in chemical engineering.

In this paper we consider the following mixed problem: (∂r/∂t)(x,t)−(∂/∂x)[v(x,t)(1−r(x,t))]=0, (∂v/∂t)(x,t)+12(∂/∂x)v2(x,t)−c0(∂r/∂x)(x,t)=f(r(x,t),v(x,t)), v(x,0)=v0(x), r(x,0)=r0(x) for x>0, v(0,t)=v1 for t>0, where v1 is a constant value and f(r,v) is defined on a bounded domain A in the (r,v)-plane. It is assumed that there is a constant M depending on the domain A and the parameters of f such that −M≤fv(r,v)≤0 for (r,v)∈A. Moreover f(r,v)=0 defines a curve v=v(r) in the domain A and v1 is chosen such that v=v1 intersects with v=v(r), in A, exactly once. For this problem we use a Glimm type scheme to approximate the solutio