Well-posedness of dual-phase-lagging heat conduction equation: higher dimensions

The dual-phase-lagging heat conduction equation is shown to be of one unique solution for a finite region of dimension n (n⩾2) under Dirichlet, Neumann or Robin boundary conditions. The solution is also found to be stable with respect to initial conditions. The work is of fundamental importance in applying the dual-phase-lagging model for the microscale heat conduction of high-rate heat flux.