Computable analysis of a boundary‐value problem for the generalized KdV–Burgers equation. (14th July 2014)

• Record Type: Journal Article
• Authors: Lu, Dianchen; Chen, Chenxia
• Is Part Of: Mathematical methods in the applied sciences. Volume 38:Number 11(2015:Jul. 30)
• Page Start: 2243
• Page End: 2249
• Publication Date: 2014-07-14
• Subjects: Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3218
• Languages: English
• ISSNs: 0170-4214

Abstract

<abstract abstract-type="main" id="mma3218-abs-0001"> <title> <x xml:space="preserve">Abstract</x> </title> <p id="mma3218-para-0001">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 <italic>H</italic>^{3<italic>m</italic> − 1}(<italic>R</italic>⁺) × <italic>H</italic>^{<italic>m</italic>}(0, <italic>T</italic>)→<italic>C</italic>([0, <italic>T</italic>];<italic>H</italic>^{3<italic>m</italic> − 1}(<italic>R</italic>⁺)) 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 <italic>m</italic> ≥ 2, and computable real number <italic>T</italic> &gt; 0. Copyright © 2014 John Wiley &amp; Sons, Ltd.</p> </abstract>