DECAY RATES FOR THE MOORE-GIBSON-THOMPSON EQUATION WITH MEMORY

被引:25
作者
Bounadja, Hizia [1 ]
Houari, Belkacem Said [2 ]
机构
[1] Ferhat Abbas Univ, Setif 19000, Algeria
[2] Univ Sharjah, Coll Sci, Dept Math, POB 27272, Sharjah, U Arab Emirates
关键词
Moore-Gibson-Thompson equation; memory kernel; energy method; exponential decay; polynomial decay; regularity loss; STABILITY; MODEL;
D O I
10.3934/eect.2020074
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The main goal of this paper is to investigate the existence and stability of the solutions for the Moore-Gibson-Thompson equation (MGT) with a memory term in the whole spaces RN. The MGT equation arises from modeling high-frequency ultrasound waves as an alternative model to the well-known Kuznetsov's equation. First, following [8] and [26], we show that the problem is well-posed under an appropriate assumption on the coefficients of the system. Then, we built some Lyapunov functionals by using the energy method in Fourier space. These functionals allows us to get control estimates on the Fourier image of the solution. These estimates of the Fourier image together with some integral inequalities lead to the decay rate of the L-2-norm of the solution. We use two types of memory term here: type I memory term and type III memory term. Decay rates are obtained in both types. More precisely, decay rates of the solution are obtained depending on the exponential or polynomial decay of the memory kernel. More importantly, we show stability of the solution in both cases: a subcritical range of the parameters and a critical range. However for the type I memory we show in the critical case that the solution has the regularity-loss property.
引用
收藏
页码:431 / 460
页数:30
相关论文
共 50 条
[31]   SPECTRAL ANALYSIS AND EXPONENTIAL STABILITY OF A MOORE-GIBSON-THOMPSON EQUATION [J].
Bezerra, Flank ;
Santos, Lucas ;
Silva, Maria ;
takaessu Jr, Carlos .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2024,
[32]   SOLVABILITY OF THE MOORE-GIBSON-THOMPSON EQUATION WITH VISCOELASTIC MEMORY TYPE II AND INTEGRAL CONDITION [J].
Boulaaras, Salah ;
Choucha, Abdelbaki ;
Ouchenane, Djamel ;
Abdalla, Mohamed ;
Vazquez, Aldo Jonathan Munoz .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2023, 16 (06) :1216-1241
[33]   Exterior controllability properties for a fractional Moore-Gibson-Thompson equation [J].
Lizama, Carlos ;
Warma, Mahamadi ;
Zamorano, Sebastian .
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2022, 25 (03) :887-923
[34]   The Cauchy problem for the Moore-Gibson-Thompson equation in the dissipative case [J].
Chen, Wenhui ;
Ikehata, Ryo .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 292 :176-219
[35]   HOLDER REGULARITY FOR THE MOORE-GIBSON-THOMPSON EQUATION WITH INFINITE DELAY [J].
Abadias, Luciano ;
Lizama, Carlos ;
Murillo-Arcila, Marina .
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2018, 17 (01) :243-265
[36]   Well-posedness and long time behavior for a general class of Moore-Gibson-Thompson equations with a memory [J].
Nicaise, Serge ;
Bounadja, Hizia .
PORTUGALIAE MATHEMATICA, 2021, 78 (3-4) :391-422
[37]   On long-time behavior of Moore-Gibson-Thompson equation with localized and degenerate memory effect [J].
Zhang, Hui .
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2021, 72 (02)
[38]   On long-time behavior of Moore-Gibson-Thompson equation with localized and degenerate memory effect [J].
Hui Zhang .
Zeitschrift für angewandte Mathematik und Physik, 2021, 72
[39]   Moore–Gibson–Thompson equation with memory, part I: exponential decay of energy [J].
Irena Lasiecka ;
Xiaojun Wang .
Zeitschrift für angewandte Mathematik und Physik, 2016, 67
[40]   Controllability results for the Moore-Gibson-Thompson equation arising in nonlinear acoustics [J].
Lizama, Carlos ;
Zamorano, Sebastian .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2019, 266 (12) :7813-7843