共查询到20条相似文献,搜索用时 0 毫秒
1.
吴舜堂 《数学物理学报(B辑英文版)》2011,31(4):1436-1448
The initial boundary value problem for a viscoelastic equation | u t | ρ u tt △u-△u tt + t 0 g(ts)△u(s)ds + | u t | m u t = | u | p u in a bounded domain is considered, where ρ, m, p > 0 and g is a nonnegative and decaying function. The general uniform decay of solution energy is discussed under some conditions on the relaxation function g and the initial data by adopting the method of [14, 15, 19]. This work generalizes and improves earlier results in the literature. 相似文献
2.
In this paper, we consider a system of coupled quasilinear viscoelastic equations with nonlinear damping. We use the perturbed energy method to show the general decay rate estimates of energy of solutions, which extends some existing results concerning a general decay for a single equation to the case of system, and a nonlinear system of viscoelastic wave equations to a quasilinear system. 相似文献
3.
本文讨论了来自于神经传播和具粘性效应的杆的纵振动问题的一类具非线性阻尼的拟线性双曲型方程的初边值问题解的存在唯一性。所用的方法是能量估计和Pazy的半解方法。 相似文献
4.
In this article, we show large time behavior of weak solutions to the Cauchy problem of the Navier-Stokes equations with damping α|u|β-1u (α0). 相似文献
5.
《数学物理学报(B辑英文版)》2015,(5)
A viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources is considered in a bounded domain. Under appropriate assumptions imposed on the source and the damping, we establish uniform decay rate of the solution energy in terms of the behavior of the nonlinear feedback and the relaxation function, without setting any restrictive growth assumptions on the damping at the origin and weakening the usual assumptions on the relaxation function. 相似文献
6.
The aim of this paper is to establish a general decay result for a one-dimensional porous elastic system with different speeds of wave propagation in the presence of macrotem- perature effect and visco-porous dissipation. 相似文献
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8.
具非线性边界条件的拟线性抛物型方程解的Blow-up 总被引:9,自引:1,他引:8
本文考虑一类具非线性边界条件的拟线性抛物方程初边值问题解的整体性态 .通过构造与解有关的适当积分 ,利用“凸性方法”及非线性抛物型方程的极大值原理 ,证明了在某些条件下 ,问题的光滑解u(x ,t)只能在一个有界区间 (0 ,T0 )中存在 ,即有 :limt→T-0sup‖u(· ,t)‖ ∞ =+∞ . 相似文献
9.
Sun Hye PARK 《数学物理学报(B辑英文版)》2014,(5):1395-1403
In this paper, we investigate the influence of boundary dissipation on the de-cay 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
10.
DECAY RATES AND CONVERGENCE OF SOLUTIONS TO SYSTEM OF ONE-DIMENSIONAL VISCOELASTIC MODEL WITH DAMPING 总被引:1,自引:0,他引:1
This paper considers the asymptotic behavior of solutions to the system of onedimensional viscoelastic model with damping and prove that the corresponding solutions time-asymptotically behave like nonlinear diffusion wave as in [4,11]. In addition, It is also shown that the system of one-dimensional viscoelastic model with damping is a viscosity approximation of a hyperbolic conservation laws with damping. 相似文献
11.
This paper considers the asymptotic behavior of solutions to the system of one-dimensional viscoelastic model with damping and prove that the corresponding solutions time-asymptotically behave like nonlinear diffusion wave as in [4,11]. In addition, It is also shown that the system of one-dimensional viscoelastic model with damping is a viscosity approximation of a hyperbolic conservation laws with damping. 相似文献
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13.
This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the multi-dimensional half space R n + : u tt u + u t + divf (u) = 0, t > 0, x = (x 1 , x ′ ) ∈ R n + := R + × R n 1 , u(0, x) = u 0 (x) → u + , as x 1 → + ∞ , u t (0, x) = u 1 (x), u(t, 0, x ′ ) = u b , x ′ = (x 2 , x 3 , ··· , x n ) ∈ R n 1 . (I) For the non-degenerate case f ′ 1 (u + ) < 0, it was shown in [10] that the above initialboundary value problem (I) admits a unique global solution u(t, x) which converges to the corresponding planar stationary wave φ(x 1 ) uniformly in x 1 ∈ R + as time tends to infinity provided that the initial perturbation and/or the strength of the stationary wave are sufficiently small. And in [10] Ueda, Nakamura, and Kawashima proved the algebraic decay estimates of the tangential derivatives of the solution u(t, x) for t → + ∞ by using the space-time weighted energy method initiated by Kawashima and Matsumura [5] and improved by Nishihkawa [7]. Moreover, by using the same weighted energy method, an additional algebraic convergence rate in the normal direction was obtained by assuming that the initial perturbation decays algebraically. We note, however, that the analysis in [10] relies heavily on the assumption that f ′ (u) < 0. The main purpose of this paper isdevoted to discussing the case of f ′ 1 (u b ) ≥ 0 and we show that similar results still hold for such a case. Our analysis is based on some delicate energy estimates. 相似文献
14.
In this paper,we present a column-secant modification of the SCC method,which is called the CSSCC method.The CSSCC method uses function values more efficiently than the SCC method,and it is shown that the CSSCC method has better local q-convergence and r-convergence rates than the SCC method.The numerical results show that the CSSCC method is competitive with some well known methods for some standard test problems. 相似文献
16.
本文首先根据Runge-Kutta方法的思想,结合Newton迭代法,提出了一类带参数的解非线性方程组F(x)=0的迭代算法,然后基于解非线性方程f(x)=0的King算法,给出第二类解非线性方程组的迭代算法,收敛性分析表明这两类算法都是五阶收敛的.其次给出了本文两类算法的效率指数,以及一些已知算法的效率指数,并且将本文算法的效率指数与其它方法进行详细的比较,通过效率比率R_(i,j)可知本文算法具有较高的计算效率.最后给出了四个数值实例,将本文两类算法与现有的几种算法进行比较,实验结果说明本文算法收敛速度快,迭代次数少,有明显的优势. 相似文献
17.
A MODIFIED LEVENBERG-MARQUARDT ALGORITHM FOR SINGULAR SYSTEM OF NONLINEAR EQUATIONS 总被引:12,自引:0,他引:12
Jin-yanFan 《计算数学(英文版)》2003,21(5):625-636
Based on the work of paper,we propose a modified Levenberg-Marquardt algoithm for solving singular system of nonlinear equations F(x)=0,where F(x):R^n→R^n is continuously differentiable and F‘(x)is Lipschitz continuous.The algorithm is equivalent to a trust region algorithm in some sense,and the global convergence result is given.The sequence generated by the algorithm converges to the solution quadratically,if ||F(x)||2 provides a local error bound for the system of nonlinear equations.Numerical results show that the algorithm performs well. 相似文献
18.
Shun-Tang Wu 《数学物理学报(B辑英文版)》2012,(6):2237-2246
The nonlinear viscoelastic wave equation |ut|ρ utt u utt + t 0 g(t s) u(s)ds + |u|p u = 0,in a bounded domain with initial conditions and Dirichlet boundary conditions is considered.We prove that,for a class of kernels g which is singular at zero,the exponential decay rate of the solution energy.The result is obtained by introducing an appropriate Lyapounov functional and using energy method similar to the work of Tatar in 2009.This work improves earlier results. 相似文献
19.
In this article, we study the large-time behavior of energy for a N-dimensional dissipative anisotropic elastic system. By means of multiplicative techniques, energy method, and Zuazua’s estimate technique, we prove the decay property of energy for anisotropic elastic system. 相似文献
20.
本文研究求解R(α,β1,β2,γ)类非线性中立型延迟积分微分方程的一般线性方法的数值稳定性,获得了代数稳定的一般线性方法稳定及渐近稳定的条件,最后的数值试验验证了所获理论的正确性.
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