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

Abstract 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.

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