Turing Computability of the Solution Operator of the Cauchy Problem for 7-order Dispersion Equation

摘要

The computability of the solution operator of the Cauchy problem for 7-order dispersion equation is studied in this paper. A nonlinear map K_R : H~S → C (R;H~S (R)) is denned from the initial value φ to the solution u, and then the type-2 theory of effectivity, functional analysis and Sobolev space are used to prove that when s ＞ -5/8, the solution operator of the Cauchy problem for 7-order dispersion equation is computable. The conclusion enriches the theories of computability.