Three-Dimensional and One-Dimensional Models for Cylinder

AUTHOR(S):

Andris Buikis, Margarita Buike, Raimonds Vilums

TITLE

Three-Dimensional and One-Dimensional Models for Cylinder

ABSTRACT

In this paper, we develop mathematical models for 3-D, 2-D and one-dimensional hyperbolic heat equations (wave equation or telegraph equation) with inner source power, and construct their analytical solutions for the determination of the initial heat flux for cylindrical sample. In some cases, we give expression of wave energy. Some solutions of time inverse problems are obtained in the form of the first kind Fredholm integral equation, but others have been obtained in closed analytical form as series. We considered both direct and inverse problems at the time.

KEYWORDS

Hyperbolic Equation, Ocean Energy, Steel Quenching, Green Function, Exact Solution, Inverse Problem, Fredholm integral equation, Series

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Cite this paper

Andris Buikis, Margarita Buike, Raimonds Vilums. (2017) Three-Dimensional and One-Dimensional Models for Cylinder. International Journal of Mathematical and Computational Methods, 2, 89-98