| Abstract: | 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. |
