On the dead-core rates for a parabolic equation with strong absorption

[[journaltype]]國內[[ispeerreviewed]]Y[[countrycodes]]TW

Mean curvature flow closes open ends of noncompact surfaces of rotation

We discuss the motion of noncompact axisymmetric hypersurfaces Tt volved by mean curvature flow. Our study provides a class of hypersurfaces hat share the same quenching time with that of the shrinking ylinder evolved by the flow and prove that they tend to a smooth hypersurface aving no pinching neck and having closed ends at infinity of the xis of rotation as the quenching time is approached. Moreover, they are ompletely characterized by a condition on initial hypersurface

Quenching for a reaction-diffusion equation with weak singularities

This paper studies the following reaction-diffusion equation with a weak singular boundary condition. The primary objective for this problem is to analyze the quenching properties. It is obtained that finite time quenching occurs on the left boundary, the time derivative of the solution blows up at the same time and also quenching rate estimates of the solution of the eqaution kt(x, t) = kxx(x, t) + ln αk(x, t), (x, t) ∈ (0, 1) × (0, T) with kx (0, t) = − ln βk(0, t), kx (1, t) = 0, t ∈ (0, T) and initial function k (x, 0) = k0 (x) with [0, 1] → (0, 1) where 0 < α, β < 1 and T is a finite time