Critical Speed for Quenching
W. E. Olmstead, Catherine Roberts · 2001
A one-dimensional heat equation with a nonlinear, concentrated quenching source that moves with constant speed through a diffusive medium is examined. Bounds are established for a critical speed above which quenching will not occur. When quenching does occur, bounds are given for the quenching time. For the special case of a power law nonlinearity, the growth rate near quenching is derived. The analysis is conducted in the context of a nonlinear Volterra integral equation that is equivalent to the initial-boundary value problem.