The Computability of the Initial Value Problem of Camassa-Holm Equation on Turing

摘要

In this paper we study the computability of the solution operator initial value problem of Camassa-Holm equation. Define a nonlinear map K from the initial date to the solution. By using Sobolve spaces and Type-2 theory of effectivity, we proved that for s >3/2 the map K is Turing computable and thus enrich the theory of computability on nonlinear equation''s solution.