Computable analysis of a boundary-value problem for the generalized KdV-Burgers equation

In this paper, we investigate the computability of the solution operator of the generalized KdV-Burgers equation with initial-boundary value problem. Here, the solution operator is a nonlinear map H3m - 1(R+) x H-m(0,T)C([0,T];H3m - 1(R+)) from the initial-boundary value data to the solution of the equation. By a technique that is widely used for the study of nonlinear dispersive equation, and using the type 2 theory of effectivity as computable model, we prove that the solution map is Turing computable, for any integer m2, and computable real number T > 0. Copyright (c) 2014 John Wiley & Sons, Ltd.