Local and non‐local boundary quenching
Catherine Roberts, W. E. Olmstead · Mathematical Methods in the Applied Sciences · 1999
The quenching problem is examined for a one-dimensional heat equation with a non-linear boundary condition that is of either local or non-local type. Sufficient conditions are derived that establish both quenching and non-quenching behaviour. The growth rate of the solution near quenching is also given for a power-law non-linearity. The analysis is conducted in the context of a nonlinear Volterra integral equation that is equivalent to the initial–boundary value problem. Copyright © 1999 John Wiley & Sons, Ltd.