Computable analysis of a boundary‐value problem for the generalized KdV–Burgers equation |
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| Authors: | Dianchen Lu Chenxia Chen |
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| Affiliation: | Faculty of Science, Jiangsu University, Xuefu Road 301, Zhenjiang, Jiangsu, 212013, China |
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| Abstract: | 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+) × Hm(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 m ≥ 2, and computable real number T > 0. Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | generalized KdV‐B equation initial‐boundary problem solution operator computability type 2 theory of effectivity subclass03D10 |
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