An analytic solution of the axisymmetric hyperbolic heat equation (Q2713906)

The authors simulate the process of extinguishing an electric arc with the generalized Fourier equation. In the axisymmetric case this model leads to the boundary value problem NEWLINE\[NEWLINE \begin{gathered} \alpha{\partial^2 T\over\partial t^2} +{\partial T\over\partial t}= {k\over r}{\partial\over\partial r}\left(r{\partial T\over\partial r}\right)\quad (T(r,t) \text{ is a~temperature of an arc}, \alpha>0), \\ T(r,0)=\varphi_1(r),\quad {\partial T\over\partial t}(r,0)=\varphi_2(r), \\ {\partial T\over\partial r}(0,t)=0,\quad T(1,t)=\text{const}. \end{gathered} NEWLINE\]NEWLINE The authors construct an~explicit solution to this boundary value problem; moreover, they give results of some numerical calculations.NEWLINENEWLINEFor the entire collection see [Zbl 0956.00039].