A uniqueness theorem for nonlinear hyperbolic systems of elasticity and electromagnetism (Q1119830)

In this paper a uniqueness theorem for solutions \(u\in L^ p(\Omega \times (0,T),{\mathbb{R}}^ m)\) of an initial-boundary value problem to the quasilinear hyperbolic system \[ \frac{\partial}{\partial t}a(u)+\sum^{n}_{i=1}B^ iu_{x_ i}=f \] is proved. The entropy condition used is \[ (u^ i(x,t+h)-u^ i(x,t))/h\geq -k(t) \] for some \(k\in L^ 1([0,T];{\mathbb{R}}^+)\) and all \(i=1,...,m\).