Upper bounds for fundamental solutions to non-local diffusion equations with divergence free drift

被引：14

作者：

Maekawa, Yasunori ^{[1
]}

Miura, Hideyuki ^{[2
]}

机构：

[1] Kobe Univ, Grad Sch Sci, Dept Math, Kobe, Hyogo 6578501, Japan

[2] Osaka Univ, Grad Sch Sci, Dept Math, Toyonaka, Osaka 5600043, Japan

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2013年 / 264卷 / 10期

关键词：

Non-local diffusion; Divergence free drift; Fundamental solutions; Pointwise upper bound; GLOBAL WELL-POSEDNESS; INEQUALITIES;

D O I：

10.1016/j.jfa.2013.02.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider some non-local diffusion equations in the presence of a divergence free drift term, where the diffusion operators are related to certain Dirichlet forms of jump type. We derive pointwise upper bounds for fundamental solutions of the equations under weak assumptions for the velocity of the drift term. Our class of the velocity includes functions with the scale-critical regularity and some growing functions at spatial infinity. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：2245 / 2268

页数：24

共 50 条

[41] Global Solutions to a Non-Local Diffusion Equation with Quadratic Non-Linearity
Krieger, Joachim
Strain, Robert M.
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2012, 37 (04) : 647 - 689
[42] Solutions of a non-local aggregation equation: Universal bounds, concavity changes, and efficient numerical solutions
Fellner, Klemens
Hughes, Barry D.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (08) : 5398 - 5429
[43] Upper and lower bounds of blow-up time in a non-local thermistor problem
Kavallaris, NI
Nikolopoulos, CV
Tzanetis, DE
Scattering and Biomedical Engineering: Modeling and Applications, 2002, : 224 - 232
[44] Multiplicity of solutions for non-local elliptic equations driven by the fractional Laplacian
Wei, Yuanhong
Su, Xifeng
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2015, 52 (1-2) : 95 - 124
[45] EXISTENCE OF ENTIRE SOLUTIONS FOR NON-LOCAL DELAYED LATTICE DIFFERENTIAL EQUATIONS
Wu, Shi-Liang
Liu, San-Yang
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2013,
[46] Regularity of Radial Extremal Solutions for Some Non-Local Semilinear Equations
Capella, Antonio
Davila, Juan
Dupaigne, Louis
Sire, Yannick
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2011, 36 (08) : 1353 - 1384
[47] Multiplicity of solutions for non-local elliptic equations driven by the fractional Laplacian
Yuanhong Wei
Xifeng Su
Calculus of Variations and Partial Differential Equations, 2015, 52 : 95 - 124
[48] Properties of positive solutions for non-local reaction-diffusion problems
Wang, MX
Wang, YM
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 1996, 19 (14) : 1141 - 1156
[49] Spreading Properties for Non-autonomous Fisher–KPP Equations with Non-local Diffusion
Arnaud Ducrot
Zhucheng Jin
Journal of Nonlinear Science, 2023, 33
[50] NON-LOCAL TRANSFORMATIONS AND NON-LOCAL CONSERVATION LAWS FOR FREE FIELDS
CALOGERO, F
NUOVO CIMENTO, 1961, 20 (02): : 297 - +

← 1 2 3 4 5 →