On solutions of space-fractional diffusion equations by means of potential wells

被引：29

作者：

Fu, Yongqiang ^{[1
]}

Pucci, Patrizia ^{[2
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

[2] Univ Perugia, Dipartimento Matemat & Informat, I-06123 Perugia, Italy

来源：

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS | 2016年 / 70期

基金：

中国国家自然科学基金;

关键词：

potential wells; space-fractional wave equations; global solutions; fractional Sobolev spaces; NONLINEAR HYPERBOLIC-EQUATIONS; WAVE-EQUATIONS; OPERATORS; ENERGY; TERMS;

D O I：

10.14232/ejqtde.2016.1.70

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the initial boundary value problem of space-fractional diffusion equations. First, we introduce a family of potential wells. Then we show the existence of global weak solutions, provided that the initial energy J (u(0)) is positive and less than the potential well depth d. Finally, we establish the vacuum isolating and blow up of strong solutions.

引用

页数：17

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