General decay rate of a variable coefficient wave equation with boundary viscoelastic damping

被引：0
作者：
Liu, Yu-Xiang [1 ]
机构：
[1] Qingdao Univ Technol, Sch Sci, Qingdao 266520, Shandong, Peoples R China
来源：
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK | 2025年 / 105卷 / 02期
基金：
中国国家自然科学基金;
关键词：
2ND-ORDER EVOLUTION-EQUATIONS; UNIFORM DECAY; MEMORY CONDITIONS; GLOBAL EXISTENCE; KIRCHHOFF TYPE; STABILITY;
D O I：
10.1002/zamm.202400655
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the general decay of wave equation with variable coefficients and boundary viscoelastic damping. Applying the Riemannian geometry method and convex analysis, we establish the energy decay rate which is given by solutions of a first-order nonlinear, dissipative ordinary differential equation under a wider assumption of the viscoelastic damping and some conditions on the coefficient matrix.
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页数：17
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共 38 条
[1]  
Pruss J., Evolutionary integral equations and applications, Monographs in Mathematics, 87, (1993)
[2]  
Eden A., Foias C., Nicolaenko B., Temam R., Exponential attractors for dissipative evolution equations, RAM: Research in Applied Mathematics, 37, (1994)
[3]  
Aassila M., Cavalcanti M.M., Soriano J.A., Asymptotic stability and energy decay rates for solutions of the wave equation with memory in a star-shaped domain, SIAM J. Control Optim., 38, 5, pp. 1581-1602, (2000)
[4]  
Aassila M., Cavalcanti M.M., Domingos Cavalcanti V.N., Existence and uniform decay rate of the wave equation with nonlinear boundary damping and boundary memory source term, Calc. Var., 15, pp. 155-180, (2002)
[5]  
Fatiha A.-B., Cannarsa P., Sforza D., Decay estimates for second order evolution equations with memory, J. Funct. Anal., 254, 5, pp. 1342-1372, (2011)
[6]  
Fan S., A new general decay rate of wave equation with memory-type boundary control, Math. Probl. Eng., 2021, pp. 1-11, (2021)
[7]  
Fan S., Feng B., Memory-type boundary stabilization of a transmission problem for the Kirchhoff wave equations, Math. Method Appl. Sci., 45, pp. 8179-8192, (2022)
[8]  
Cavalcanti M.M., Cavalcanti V.N.D., Filho J.S.P., Soriano J.A., Existence and uniform decay of solutions of a degenerate equation with nonlinear boundary damping and boundary memory source term, Nonlinear Anal. Theory Methods Appl., 38, 3, pp. 281-294, (1999)
[9]  
Cavalcanti M.M., Domingos Cavalcanti V.N., Santos M.L., Existence and uniform decay rates of solutions to a degenerate system with memory conditions at the boundary, Appl. Math. Comput., 150, pp. 439-465, (2004)
[10]  
Cavalcanti M.M., Guesmia A., General decay rates of solutions to a nonlinear wave equation with boundary conditions of memory type, Differ. Inter. Equ., 18, pp. 583-600, (2005)
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