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.
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页码：2963 / 2986
页数：24
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