Polynomial Decay of Solutions to the Cauchy Problem for a Petrovsky-Petrovsky System in Rn

被引：0

作者：

Beniani, Abderrahmane ^{[1
]}

Benaissa, Abbes ^{[1
]}

Zennir, Khaled ^{[2
]}

机构：

[1] Univ Djillali Liabes Sidi Bel Abbes, Lab ACEDP, BP 89, Sidi Bel Abbes 22000, Algeria

[2] 20 Aout 55 Univ, Lab LAMAIH, Skikda 21000, Algeria

来源：

ACTA APPLICANDAE MATHEMATICAE | 2016年 / 146卷 / 01期

关键词：

Petrovsky equation; Memory; Coupled system; Polynomial decay; Weighted spaces; STABILIZATION; EQUATIONS; STABILITY;

D O I：

10.1007/s10440-016-0058-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper describes a polynomial decay rate of solution for a coupled system of Petrovsky equations in with infinite memory acting in the first equation. The weighted spaces and results in Guesmia (Appl. Anal. 94(1):184-217, 2015) are also used. The main contributions here is to show that the infinite memory lets our problem still dissipative and that the system is not exponentially stable in spite of the kernel in the memory term is sub-exponential.

引用

页码：67 / 79

页数：13

共 50 条

[21] Numerical Solution to the Dirichlet Control Problem on a Part of the Boundary for the Petrovsky system
Dryazhenkov, A.
Artemyeva, L.
IFAC PAPERSONLINE, 2018, 51 (32): : 748 - 753
[22] Decay rate of solutions to the Cauchy problem for a coupled system of viscoelastic wave equations with a strong delay in Rn
Chaili, Amina
Belhadji, Bochra
Beniani, Abderrahmane
STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, 2023, 68 (04): : 895 - 905
[23] Blow-Up of Solutions for a System of Petrovsky Equations with an Indirect Linear Damping
Liu, Wenjun
ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 2013, 68 (05): : 343 - 349
[24] Existence and Asymptotic Behavior of Global Solutions bf for Some Nonlinear Petrovsky System
Ye, Yaojun
BULLETIN MATHEMATIQUE DE LA SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE, 2016, 59 (04): : 389 - 398
[25] Polynomial-exponential stability and blow-up solutions to a nonlinear damped viscoelastic Petrovsky equation
Peyravi A.
Tahamtani F.
SeMA Journal, 2020, 77 (2) : 181 - 201
[26] A PRINCIPLE OF LOCALIZATION FOR SOLUTION OF THE CAUCHY-PROBLEM OF SYSTEMS PARABOLIC AFTER PETROVSKY IN A CLASS OF GENERALIZED-FUNCTIONS
GORODETSKY, VV
DOPOVIDI AKADEMII NAUK UKRAINSKOI RSR SERIYA A-FIZIKO-MATEMATICHNI TA TECHNICHNI NAUKI, 1984, (10): : 5 - 7
[27] Asymptotic stability and blow up of solutions for a Petrovsky inverse source problem with dissipative boundary condition
Tahamtani, F.
Shahrouzi, M.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2013, 36 (07) : 829 - 839
[28] The Cauchy problem and decay rates for strong solutions of a Boussinesq system
Gonzalez, Francisco Guillen
Da Rocha, Marcio Santos
Medar, Marko Rojas
ABSTRACT AND APPLIED ANALYSIS, 2005, (07) : 757 - 766
[29] Global existence and blow-up of solutions for a strongly damped Petrovsky system with nonlinear damping
Li, Gang
Sun, Yanan
Liu, Wenjun
APPLICABLE ANALYSIS, 2012, 91 (03) : 575 - 586
[30] EXISTENCE OF GLOBAL SOLUTIONS AND DECAY ESTIMATES FOR A VISCOELASTIC PETROVSKY EQUATION WITH A DELAY TERM IN THE NON-LINEAR INTERNAL FEEDBACK
Mezouar, Nadia
Abdelli, Mama
Rachah, Amira
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2017,

← 1 2 3 4 5 →