Optimal existence and uniqueness theory for the fractional heat equation

被引：75
|
作者：
Bonforte, Matteo [1 ]
Sire, Yannick [2 ,3 ]
Luis Vazquez, Juan [1 ]
机构：
[1] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain
[2] Johns Hopkins Univ, Baltimore, MD USA
[3] Univ Aix Marseille, Marseille, France
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2017年 / 153卷
关键词：
Fractional heat equation; Existence and uniqueness theory; Optimal data; Pointwise estimates; Harnack inequalities; POROUS-MEDIUM EQUATION; NONLOCAL PARABOLIC EQUATIONS; NONLINEAR DIFFUSION; REGULARITY; OPERATORS; SPACES; KERNEL; GUIDE;
D O I：
10.1016/j.na.2016.08.027
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We construct a theory of existence, uniqueness and regularity of solutions for the fractional heat equation partial derivative(t)u + (-Delta)(s)u = 0, 0 < s < 1, posed in the whole space RN with data in a class of locally bounded Radon measures that are allowed to grow at infinity with an optimal growth rate. We consider a class of nonnegative weak solutions and prove that there is an equivalence between nonnegative data and solutions, which is given in one direction by the representation formula, in the other one by the initial trace. We review many of the typical properties of the solutions, in particular we prove optimal pointwise estimates and new Harnack inequalities. (C) 2016 Elsevier Ltd. All rights reserved.
引用
收藏
页码：142 / 168
页数：27
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