The wave propagator is turing computable

摘要

Pour-El/Richards [PER89] and Pour-El/Zhong [PEZ97] have shown that there is a computable initial condition f for the three dimensional wave equation u_tt=#DLETA#u,u(0,x)=f(x),u_t(0,x)=0, t IR,x IR~3,such that the unique solution is not computable.This very remark-able result might indicate that the physical process of wave prpagatioo is not computable and possibly disprove Truing's.In this paper computability of wave propagation is studied in detail.Concepts from TTE,concepts on the sapces under consideration.It is shown that the solution operator of the Cauchy problem is computable on continuously differentiable initial conditions.where one order of differentiability is lost.The solution operator is also computable on Sobolev spaces.Finally the results are interpreted in a simple physical model.