Decay estimates for evolution equations with classical and fractional time-derivatives

Elisa Affili, Enrico Valdinoci

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Using energy methods, we prove some power-law and exponential decay estimates for classical and nonlocal evolutionary equations. The results obtained are framed into a general setting, which comprise, among the others, equations involving both standard and Caputo time-derivative, complex valued magnetic operators, fractional porous media equations and nonlocal Kirchhoff operators. Both local and fractional space diffusion are taken into account, possibly in a nonlinear setting. The different quantitative behaviours, which distinguish polynomial decays from exponential ones, depend heavily on the structure of the time-derivative involved in the equation.

Original languageEnglish
Pages (from-to)4027-4060
Number of pages34
JournalJournal of Differential Equations
Volume266
Issue number7
DOIs
Publication statusPublished - 15 Mar 2019

Fingerprint

Decay Estimates
Evolution Equation
Fractional
Derivatives
Derivative
Polynomial Decay
Porous materials
Porous Medium Equation
Polynomials
Energy Method
Operator
Exponential Decay
Power Law

Cite this

@article{70ef7fee27a14c36958b793f7f772c47,
title = "Decay estimates for evolution equations with classical and fractional time-derivatives",
abstract = "Using energy methods, we prove some power-law and exponential decay estimates for classical and nonlocal evolutionary equations. The results obtained are framed into a general setting, which comprise, among the others, equations involving both standard and Caputo time-derivative, complex valued magnetic operators, fractional porous media equations and nonlocal Kirchhoff operators. Both local and fractional space diffusion are taken into account, possibly in a nonlinear setting. The different quantitative behaviours, which distinguish polynomial decays from exponential ones, depend heavily on the structure of the time-derivative involved in the equation.",
author = "Elisa Affili and Enrico Valdinoci",
year = "2019",
month = "3",
day = "15",
doi = "10.1016/j.jde.2018.09.031",
language = "English",
volume = "266",
pages = "4027--4060",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Academic Press",
number = "7",

}

Decay estimates for evolution equations with classical and fractional time-derivatives. / Affili, Elisa; Valdinoci, Enrico.

In: Journal of Differential Equations, Vol. 266, No. 7, 15.03.2019, p. 4027-4060.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Decay estimates for evolution equations with classical and fractional time-derivatives

AU - Affili, Elisa

AU - Valdinoci, Enrico

PY - 2019/3/15

Y1 - 2019/3/15

N2 - Using energy methods, we prove some power-law and exponential decay estimates for classical and nonlocal evolutionary equations. The results obtained are framed into a general setting, which comprise, among the others, equations involving both standard and Caputo time-derivative, complex valued magnetic operators, fractional porous media equations and nonlocal Kirchhoff operators. Both local and fractional space diffusion are taken into account, possibly in a nonlinear setting. The different quantitative behaviours, which distinguish polynomial decays from exponential ones, depend heavily on the structure of the time-derivative involved in the equation.

AB - Using energy methods, we prove some power-law and exponential decay estimates for classical and nonlocal evolutionary equations. The results obtained are framed into a general setting, which comprise, among the others, equations involving both standard and Caputo time-derivative, complex valued magnetic operators, fractional porous media equations and nonlocal Kirchhoff operators. Both local and fractional space diffusion are taken into account, possibly in a nonlinear setting. The different quantitative behaviours, which distinguish polynomial decays from exponential ones, depend heavily on the structure of the time-derivative involved in the equation.

UR - http://www.scopus.com/inward/record.url?scp=85054130532&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2018.09.031

DO - 10.1016/j.jde.2018.09.031

M3 - Article

VL - 266

SP - 4027

EP - 4060

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 7

ER -