Estimating the Time of a Thermal Meltdown

The paper investigates the transient behavior of a nonlinear heat process, described by a second order, nonlinear partial differential equation with given boundary-and initial conditions. The PDE may describe various physical processes, but we interpret in this case as a thermal process with exponential inner heat source. It is already known that for certain parameter values and boundary conditions the process may become unstable (Vajta, 2003 and 2004) leading to a thermal meltdown. What is not yet known is how much time may elapse until the thermal meltdown happens for given parameters and BC´s. We describe an approximate solution which makes time estimation possible. The proposed method can also be applied for a wider class of similar problems