Computing Solutions of Symmetric Hyperbolic Systems of PDE's

We study the computability properties of symmetric hyperbolic systems of PDE's , A=A∗>0, , with the initial condition u|t=0=φ(x1,…,xm). Such systems first considered by K.O. Friedrichs can be used to describe a wide variety of physical processes. Using the difference equations approach, we prove computability of the operator that sends (for any fixed computable matrices A,B1,…,Bm satisfying some natural conditions) any initial function φ∈Ck+1(Q,Rn), k≥1, to the unique solution u∈Ck(H,Rn), where Q=m[0,1] and H is the nonempty domain of correctness of the system.