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.
|Original language||English (US)|
|Number of pages||20|
|Journal||Mathematical Methods in the Applied Sciences|
|State||Published - Nov 10 1999|
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