Turing Computability of the Solution Operator of the Initial Value Problem for Fifth-order Camassa-Holm Equation
نویسندگان
چکیده
The computability of the solution operator of the Cauchy problem for the Fifth-order CamassaHolm equation is studied in this paper. Firstly, a nonlinear map KR : H → C (R;H (R)) is defined from the initial value φ to the solution u. Then we used the relevant knowledge of type-2 theory of effectivity, functional analysis and Sobolev space to prove that when s > (6 √ 10− 17) / 4, the solution operator of the Cauchy problem the Fifth-order Camassa-Holm equation is computable. The conclusion enriches the theories of computability.
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