GENERAL INITIAL DATA FOR A CLASS OF PARABOLIC EQUATIONS INCLUDING THE CURVE SHORTENING PROBLEM

被引：2

作者：

Chou, Kai-Seng ^{[1
]}

Kwong, Ying-Chuen ^{[2
]}

机构：

[1] Chinese Univ Hong Kong, Hong Kong, Peoples R China

[2] Northern Illinois Univ, De Kalb, IL 60115 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2020年 / 40卷 / 05期

关键词：

Initial trace; curve shortening problem; porous medium equations; Widder's theorem; Cauchy problem; LEVEL SETS; BLOW-UP; SURFACES; MOTION;

D O I：

10.3934/dcds.2020157

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Cauchy problem for a class of non-uniformly parabolic equations including (4) is studied for initial data with less regularity. When m is an element of (1,2], it is shown that there exists a smooth solution for t > 0 when the initial data belongs to L-loc(p),p > 1. When m > 2, the same results holds when the initial data belongs to W-loc(1,p),p >= m(-1). An example is displayed to show that a smooth solution may not exist when the initial data is merely in L-loc(p),p > 1. Solvability of the weak solution is also studied.

引用

页码：2963 / 2986

页数：24

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