A new mathematical model of heat conduction processes

To describe heat conduction processes and diffusion, a new fourth-order partial differential equation Lu₁L₁u+₂L₂u=0, where L₂=L₁L₁ and L₁ is the classical heat conduction operator, which is invariant with respect to the Galielei group, is proposed. We also obtain an integral representation of the solution of the corresponding boundary problem and study solutions of the Cauchy problem of the traveling-wave type, as well as solutions with an exponential and peaking exponential boundary mode.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 2, pp. 237–245, February, 1990.