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