# Blow-up rates of solutions of initial-boundary value problems for a quasi-linear parabolic equation

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5 Citations (Scopus)

## Abstract

We consider initial-boundary value problems for a quasi linear parabolic equation, kt=k2(kθθ+k), with zero Dirichlet boundary conditions and positive initial data. It has known that each of solutions blows up at a finite time with the rate faster than (T−t)−1. In this paper, it is proved that supθ⁡k(θ,t)≈(T−t)−1log⁡log⁡(T−t)−1 as t↗T under some assumptions. Our strategy is based on analysis for curve shortening flows that with self-crossing brought by S.B. Angenent and J.J.L. Velázquez. In addition, we prove some of numerical conjectures by Watterson which are keys to provide the blow-up rate.

Original language English 181-271 91 Journal of Differential Equations 262 1 https://doi.org/10.1016/j.jde.2016.09.023 Published - 2017 Jan 5

## Keywords

• Curve shortening flows
• Quasi-linear parabolic equations
• Type II blow-up

## ASJC Scopus subject areas

• Analysis
• Applied Mathematics

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