Large exponent behavior for power-type nonlinear evolution equations and applications

Abstract

Motivated by math models of image denoising and collapsing sandpiles, we are concerned with asymptotic behavior for a class of fully nonlinear power-type evolution equations in one space dimension as the exponent tends to infinity. It turns out that an initial layer appears in the large exponent limit. In order to examine the initial layer, we rescale the solution by stretching the time variable and study a fully nonlinear equation with a discontinuous and unbounded parabolic operator. We establish uniqueness and existence of viscosity solutions to this limit equation.