Turing Computability of the Solution Operator of the Cauchy Problem for Nonlinear Davey-Stewartson Equation

Abstract:

The computability of the solution operator of the Cauchy problem for the nonlinear Davey-Stewartson equation is studied in this paper. Firstly, a nonlinear map K_RH⁵(R²)→C(R;H⁵(R²)), where H⁵(R²) is inhomogeneous Sobolev space on R², defined from the initial value Φ to the solutionu. Then we used the relevant knowledge of type-2 theory of effectivity, functional analysis and Sobolev space to prove that when s>4/7 the solution operator of the Cauchy problem for the nonlinear Davey-Stewartson equation is computable. The conclusion enriches the theories of computability.

• Periodical: Applied Mechanics and Materials (Volumes 513-517)
• Pages: 4499-4503
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.513-517.4499
• Online since: February 2014
• Authors: Dian Chen Lu*, Wen Bing Yan, Li Wu
• Keywords: Cauchy Problem, Nonlinear Davey-Stewartson Equation, Turing Computability, Type-2 Theory of Effectivity

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