Equivalence between the internal observability and exponential decay for the Moore-Gibson-Thompson equation

Applied Mathematics-A Journal of Chinese Universities - Tập 39 Số 1 - Trang 89-97 - 2024
Wenjun Liu1, Zhiyu Tu1
1School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China

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M O Alves, et al. Moore-Gibson-Thompson equation with memory in a history framework: a semigroup approach, Z Angew Math Phys, 2018, 69: 106.

A H Caixeta, I Lasiecka, V N D Cavalcanti. Global attractors for a third order in time nonlinear dynamics, J Differential Equations, 2016, 261(1): 113–147.

A H Caixeta, I Lasiecka, V N D Cavalcanti. On long time behavior of Moore-Gibson-Thompson equation with molecular relaxation, Evol Equ Control Theory, 2016, 5(4): 661–676.

J A Conejero, C Lizama, F Rodenas. Chaotic behaviour of the solutions of the Moore-Gibson-Thompson equation, Appl Math Inf Sci, 2015, 9(5): 2233–2238.

F Dell’Oro, V Pata. On a fourth-order equation of Moore-Gibson-Thompson type, Milan J Math, 2017, 85(2): 215–234.

H F Di, Y D Shang, J L Yu. Existence and uniform decay estimates for the fourth order wave equation with nonlinear boundary damping and interior source, Electron Res Arch, 2020, 28(1): 221–261.

B Feng. Well-posedness and exponential decay for laminated Timoshenko beams with time delays and boundary feedbacks, Math Methods Appl Sci, 2018, 41(3): 1162–1174.

B Feng, et al. Dynamics of laminated Timoshenko beams, J Dynam Differential Equations, 2018, 30(4): 1489–1507.

A Haraux. Une remarque sur la stabilisation de certains systemes du deuxième ordre en temps, Portugal Math, 1989, 46(3): 245–258.

P M Jordan. Nonlinear acoustic phenomena in viscous thermally relaxing fluids: Shock bifurcation and the emergence of diffusive solitons, J Acoust Soc Am, 2008, 124(4): 2491–2491.

B Kaltenbacher, I Lasiecka, R Marchand. Wellposedness and exponential decay rates for the Moore-Gibson-Thompson equation arising in high intensity ultrasound, Control Cybernet, 2011, 40(4): 971–988.

I Lasiecka. Global solvability of Moore-Gibson-Thompson equation with memory arising in nonlinear acoustics, J Evol Equ, 2017, 17(1): 411–441.

I Lasiecka, X Wang. Moore-Gibson-Thompson equation with memory, part I: exponential decay of energy, Z Angew Math Phys, 2016, 67: 17.

I Lasiecka, X Wang. Moore-Gibson-Thompson equation with memory, part II: General decay of energy, J Differential Equations, 2015, 259(12): 7610–7635.

W J Liu, Z J Chen. General decay rate for a Moore–Gibson–Thompson equation with infinite history, Z Angew Math Phys, 2020, 71(2): 2–43.

W J Liu, Z J Chen, D Q Chen. New general decay results for a Moore-Gibson-Thompson equation with memory, Appl Anal, 2020, 99(15): 2622–2640.

W J Liu, Z J Chen, Z Y Tu. New general decay result for a fourth-order Moore-Gibson-Thompson equation with memory, Electron Res Arch, 2020, 28(1): 433–457.

F Moore, W Gibson. Propagation of weak disturbances in a gas subject to relaxing effects, Journal of the Aerospace Sciences, 1960, 27: 117–127.

C Mu, J Ma. On a system of nonlinear wave equations with Balakrishnan-Taylor damping, Z Angew Math Phys, 2014, 65(1): 91–113.

M I Mustafa. Laminated Timoshenko beams with viscoelastic damping, J Math Anal Appl, 2018, 466(1): 619–641.

M I Mustafa. On the stabilization of viscoelastic laminated beams with interfacial slip, Z Angew Math Phys, 2018, 69: 33.

M Pellicer, J Solà-Morales. Optimal scalar products in the Moore-Gibson-Thompson equation, Evol Equ Control Theory, 2019, 8(1): 203–220.

A J A Ramos, et al. Equivalence between exponential stabilization and boundary observability for piezoelectric beams with magnetic effect, Z Angew Math Phys, 2019, 70: 60.

A J A Ramos, M W P Souza. Equivalence between observability at the boundary and stabilization for transmission problem of the wave equation, Z Angew Math Phys, 2017, 68:48.

P Stokes. An examination of the possible effect of the radiation of heat on the propagation of sound, Philosophical Magazine Series 4, 1851, 1(4): 305–317.

L Tebou. Equivalence between observability and stabilization for a class of second order semilinear evolution equations, Discrete Contin Dyn Syst, 2009, 2009: 744–752.

P A Thompson. Compressible-Fluid Dynamics, McGraw-Hill, New York, 1972.

Y S Zheng, W J Liu, Y D Liu. Equivalence between internal observability and exponential stabilization for suspension bridge problem, Ricerche di Matematica, 2022, 71: 711–721.