Two-dimensional non-Fourier heat conduction with arbitrary initial and periodic boundary conditions

In this paper, the (2+1)-dimensional hyperbolic heat conduction equation is analytically solved under the influence of arbitrary initial conditions for a rectangular plate with homogeneous boundary conditions of first-kind. The temperature field is obtained as a double Fourier series. The presented solution is valid even for discontinuous but integrable initial conditions. Afterwards, the solution is generalized by means of a transformation to cover problems with inhomogeneous first-kind boundary conditions. Another interesting issue is that the obtained solution can be considered as a solution to the Klein-Gordon equation under the influence of arbitrary initial conditions by means of a simple transformation.