**AUTHORS:**Andris Buikis, Margarita Buike, Raimonds Vilums

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**ABSTRACT:**
In this paper we develop mathematical models for 3-D, 2-D and one-dimensional hyperbolic heat equations (wave equation or telegraph equation) and construct their analytical solutions for the determination of the initial heat flux for rectangular samples. In some cases we give expression of wave energy. Some solutions of time inverse problems are obtained in the form of first kind Fredholm integral equation, but others has been obtained in closed analytical form. Finally, writes in one dimension intensive steel quenching model numerical results. We viewed both direct and inverse problems at the time. Are given some of the wave energy results.

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

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