A criterion of applicability of the parabolic heat conduction equation

Photoemission measurements of temperature in pulsed laser heating of various materials

“…Further heating leads to a nonlinear regime of nonequilibrium thermodynamics. It should be noted that from the point of view of the thermodynamic regimes, our data obtained for graphite agree with the results of [6]. The temperature of tungsten and of the silicon dioxide (SiO 2 ⁄ Si) film heated under similar conditions (Fig.…”

“…At the initial stage of heating one observes a linear portion on the function T(t) with ∂T ∂t = 10 7 K ⁄ s (Si) and 1.6⋅10 7 K ⁄ s (graphite). According to the thermodynamic criterion introduced in [6], in this situation where ∂ 2 T ∂t 2 = 0, a linear regime of nonequilibrium thermodynamics is being established. Here, the heating is described well by the parabolic heat conduction equation.…”

Classical Solutions of a Mixed Problem with the Zaremba Boundary Condition for a Mildly Quasilinear Wave Equation

“…Since the function f defined by the formula (6.3) is Lipschitz continuous with respect to the last three variables and infinitely differentiable ones, then a classical solution to the problem (1.1) -(1.4), (6.3) is determined by Theorem 2.1. It exists under the smoothness conditions 1 The insignificance of the relaxation effects of heat transfer can be estimated by the quantity τr∂ 2 t u/∂tu [59].…”