Computable Analysis of the Initial Value Problem for the Weak Dissipation Camassa-Holm Equation

In this paper we study the computability of the solution operator of the initial value problem of weak dissipation Camassa-Holm equation. Let K-R : H-s (R) -> C(R,H-s (R)) be a nonlinear map from the initial date phi is an element of H-s (R) to the solution u is an element of C(R,H-s (R)). By using Sobolve spaces and Type-2 theory of effectivity, we proved that, for s > 2, the map K-R is Turing computable and thus enrich the theory of computability on nonlinear equation's solution.