Computing the Solution of Cauchy Problems of a Class of Nonlinear Heat Conduction Equation on Turing Machine
Dianchen Lu, Shao Jian Song · Advanced materials research · 2013
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.