Computing the Solution of Cauchy Problems of a Class of Nonlinear Heat Conduction Equation on Turing Machine

Dian Chen Lu; Shao Jian Song

doi:10.4028/www.scientific.net/AMR.740.310

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HomeAdvanced Materials ResearchAdvanced Materials Research Vol. 740Computing the Solution of Cauchy Problems of a...

Computing the Solution of Cauchy Problems of a Class of Nonlinear Heat Conduction Equation on Turing Machine

Abstract:

The computability of the solution for the Cauchy Problems of the nonlinear Heat Conduction equation is studied in this paper. A nonlinear map is defined from the initial value to the solution . We used the relevant knowledge of type-2 theory of effectivity, functional analysis and Sobolev space to prove that when , the solution operator of the initial problem for the Heat Conduction equation is computable under certain conditions. The conclusion enriches the theories of computability.

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Periodical:

Advanced Materials Research (Volume 740)

Pages:

310-314

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.740.310

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Online since:

August 2013

Authors:

Dian Chen Lu, Shao Jian Song

Keywords:

Cauchy Problem, Computability, Nonlinear Heat Conduction Equation, Type-2 Theory of Effectivity

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