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1.
General decay of solutions of a wave equation with memory term and acoustic boundary condition 下载免费PDF全文
In this paper, the global solvability to the mixed problem involving the wave equation with memory term and acoustic boundary conditions for non‐locally reacting boundary is considered. Moreover, the general decay of the energy functionality is established by the techniques of Messaoudi. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
2.
A. Soufyane M. Afilal M. Chacha 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(11):3903-3605
In this paper we consider linear porous-thermoelasticity systems, in a bounded domain, where the memory-type damping is acting on a part of the boundary. We establish a general decay result, for which the usual exponential and polynomial decay rates are just special cases. Our work allows certain relaxation functions which are not necessarily of exponential or polynomial decay and, therefore, generalizes and improves on earlier results from the literature. 相似文献
3.
Sun Hye Park Jong Yeoul Park Yong Han Kang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2012,63(5):813-823
A Karman equation of memory type with acoustic boundary conditions is considered. This work is devoted to investigate the influence of kernel function g and prove general decay rates of solutions when g does not necessarily decay exponentially. 相似文献
4.
In this paper, we investigate the influence of boundary dissipation on the decay property of solutions for a transmission problem of Kirchhoff type wave equation with boundary memory condition. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of relaxation function. 相似文献
5.
Farida Cheheb Hanane Benkhedda Abbes Benaissa 《Mathematical Methods in the Applied Sciences》2019,42(8):2721-2733
We study a wave equation with a dynamic boundary control of diffusive type. We establish optimal and explicit energy decay formula by using resolvent estimates. Our new result generalizes and improves the earlier related results in the literature. 相似文献
6.
In this paper, we study well‐posedness and asymptotic stability of a wave equation with a general boundary control condition of diffusive type. We prove that the system lacks exponential stability. Furthermore, we show an explicit and general decay rate result, using the semigroup theory of linear operators and an estimate on the resolvent of the generator associated with the semigroup. 相似文献
7.
《Applied Mathematics Letters》2007,20(8):861-865
We derive decay rates for the energies of solutions of one-dimensional wave equations with Dirichlet boundary control. The method of proof combines multiplier techniques and the Lyapunov method. 相似文献
8.
In this paper, we consider the weak viscoelastic equation $$u_{tt} - \Delta u + \alpha(t) \int\limits_{0}^{t} g(t-s)\Delta u(s)\, {\rm d}s=0$$ with a homogeneous Dirichlet condition on a portion of the boundary and acoustic boundary conditions on the rest of the boundary. We establish a general decay result, which depends on the behavior of both α and g, by using the perturbed energy functional technique. This is an extension and improvement of the previous result from Park and Park (Nonlinear Anal 74(3):993–998, 2011) (i.e., the similar problem with ${\alpha(t) \equiv 1}$ ) to the time-dependent viscoelastic case. 相似文献
9.
10.
Jieqiong Wu Shengjia Li Shugen Chai 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(7):2213-2220
A wave equation with variable coefficients in principal part and memory conditions on the boundary is considered. The Riemannian geometry method is applied to prove the exponential decay of the energy provided the relaxation function also decays exponentially. 相似文献
11.
In this article, we study the weak dissipative Kirchhoff equation \({u_{tt}} - M\left( {\left\| {\nabla u} \right\|_2^2} \right)\Delta u + b\left( x \right){u_t} + f\left( u \right) = 0\), under nonlinear damping on the boundary \(\frac{{\partial u}}{{\partial v}} + \alpha \left( t \right)g\left( {{u_t}} \right) = 0\). We prove a general energy decay property for solutions in terms of coefficient of the frictional boundary damping. Our result extends and improves some results in the literature such as the work by Zhang and Miao (2010) in which only exponential energy decay is considered and the work by Zhang and Huang (2014) where the energy decay has been not considered. 相似文献
12.
Shun-Tang Wu 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2012,63(1):65-106
In this paper, a viscoelastic equation with nonlinear boundary damping and source terms of the form $$\begin{array}{llll}u_{tt}(t)-\Delta u(t)+\displaystyle\int\limits_{0}^{t}g(t-s)\Delta u(s){\rm d}s=a\left\vert u\right\vert^{p-1}u,\quad{\rm in}\,\Omega\times(0,\infty), \\ \qquad\qquad\qquad\qquad\qquad u=0,\,{\rm on}\,\Gamma_{0} \times(0,\infty),\\ \dfrac{\partial u}{\partial\nu}-\displaystyle\int\limits_{0}^{t}g(t-s)\frac{\partial}{\partial\nu}u(s){\rm d}s+h(u_{t})=b\left\vert u\right\vert ^{k-1}u,\quad{\rm on} \ \Gamma_{1} \times(0,\infty) \\ \qquad\qquad\qquad\qquad u(0)=u^{0},u_{t}(0)=u^{1},\quad x\in\Omega, \end{array}$$ is considered in a bounded domain ??. Under appropriate assumptions imposed on the source and the damping, we establish both existence of solutions and uniform decay rate of the solution energy in terms of the behavior of the nonlinear feedback and the relaxation function g, without setting any restrictive growth assumptions on the damping at the origin and weakening the usual assumptions on the relaxation function g. Moreover, for certain initial data in the unstable set, the finite time blow-up phenomenon is exhibited. 相似文献
13.
General decay of solutions of quasilinear wave equation with time‐varying delay in the boundary feedback and acoustic boundary conditions 下载免费PDF全文
Mi Jin Lee Jong Yeoul Park Sun‐Hye Park 《Mathematical Methods in the Applied Sciences》2017,40(12):4560-4576
In this paper, we are concerned with the general decay result of the quasi‐linear wave equation with a time‐varying delay in the boundary feedback and acoustic boundary conditions. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
14.
Salim A. Messaoudi 《Journal of Mathematical Analysis and Applications》2008,341(2):1457-1467
In this paper we consider the following viscoelastic equation:
15.
Radhouane Aounallah Salah Boulaaras Abderrahmane Zarai Bahri Cherif 《Mathematical Methods in the Applied Sciences》2020,43(12):7175-7193
The paper deals with the study of global existence of solutions and the general decay in a bounded domain for nonlinear wave equation with fractional derivative boundary condition by using the Lyaponov functional. Furthermore, the blow up of solutions with nonpositive initial energy combined with a positive initial energy is established. 相似文献
16.
《Nonlinear Analysis: Theory, Methods & Applications》2005,61(3):351-372
In this paper we prove the existence of solution and uniform decay of energy to the mixed problem for coupled wave equation of Kirchhoff-type subject to memory condition on the boundary. 相似文献
17.
M. Aassila M.M. Cavalcanti V.N. Domingos Cavalcanti 《Calculus of Variations and Partial Differential Equations》2002,15(2):155-180
We consider the nonlinear model of the wave equation
subject to the following nonlinear boundary conditions
We show existence of solutions by means of Faedo-Galerkin method and the uniform decay is obtained by using the multiplier
technique.
Received: 15 June 2000 / Accepted: 4 December 2000 / Published online: 29 April 2002 相似文献
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19.
General decay for a differential inclusion of Kirchhoff type with a memory condition at the boundary
In this article, we consider a differential inclusion of Kirchhoff type with a memory condition at the boundary. We prove the asymptotic behavior of the corresponding solutions. For a wider class of relaxation functions, we establish a more general decay result, from which the usual exponential and polynomial decay rates are only special cases. 相似文献
20.
P. Jameson Graber 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(10):3137-3148
We consider a wave equation with semilinear porous acoustic boundary conditions. This is a coupled system of second and first order in time partial differential equations, with possibly semilinear boundary conditions on the interface. The results obtained are (i) strong stability for the linear model, (ii) exponential decay rates for the energy of the linear model, and (iii) local exponential decay rates for the energy of the semilinear model. This work builds on a previous result showing generation of a well-posed dynamical system. The main tools used in the proofs are (i) the Stability Theorem of Arendt-Batty, (ii) energy methods used in the study of a wave equation with boundary damping, and (iii) an abstract result of I. Lasiecka applicable to hyperbolic-like systems with nonlinearly perturbed boundary conditions. 相似文献