共查询到20条相似文献,搜索用时 15 毫秒
1.
We study large time asymptotic behavior of solutions to the periodic problem for the nonlinear Burgers type equation
$ \left\{ {l} \psi_{t}=\psi_{xx}+\lambda \psi +\psi \psi_{x},\quad x\in \Omega, \quad t >0 , \\ \psi (0,x)=\widetilde{\psi}(x), \quad x\in \Omega, \right. $ \left\{ \begin{array}{l} \psi_{t}=\psi_{xx}+\lambda \psi +\psi \psi_{x},\quad x\in \Omega, \quad t >0 , \\ \psi (0,x)=\widetilde{\psi}(x), \quad x\in \Omega, \end{array} \right. 相似文献
2.
Rafael Carreño-Bolaños Beatriz Juarez-Campos Pavel I. Naumkin 《Studies in Applied Mathematics》2020,145(1):137-149
We study the nonlinear damped wave equation with a linear pumping and a convective nonlinearity. We consider the solutions, which satisfy the periodic boundary conditions. Our aim is to prove global existence of solutions to the periodic problem for the nonlinear damped wave equation by applying the energy-type estimates and estimates for the Green operator. Moreover, we study the asymptotic profile of global solutions. 相似文献
3.
Tatsuki Kawakami Hiroshi Takeda 《NoDEA : Nonlinear Differential Equations and Applications》2016,23(5):54
We study the Cauchy problem for a nonlinear damped wave equation. Under suitable assumptions for the nonlinearity and the initial data, we obtain the global solution which satisfies weighted L 1 and \({L^\infty}\) estimates. Furthermore, we establish the higher order asymptotic expansion of the solution. This means that we construct the nonlinear approximation of the global solution with respect to the weight of the data. Our proof is based on the approximation formula of the linear solution, which is given by Takeda (Asymptot Anal 94:1–31, 2015), and the nonlinear approximation theory for a nonlinear parabolic equation developed by Ishige et al. (J Evol Equ 14:749–777, 2014). 相似文献
4.
Tokio Matsuyama 《Transactions of the American Mathematical Society》2003,355(3):865-899
We are interested in the asymptotic behaviour of global classical solutions to the initial-boundary value problem for the nonlinear dissipative wave equation in the whole space or the exterior domain outside a star-shaped obstacle. We shall treat the nonlinear dissipative term like , , 0)$"> and prove that the energy does not in general decay. Further, we can deduce that the classical solution is asymptotically free and the local energy decays at a certain rate as the time goes to infinity.
5.
Kenji Nishihara Huijiang Zhao 《Journal of Mathematical Analysis and Applications》2006,313(2):598-610
We consider the Cauchy problem for the damped wave equation with absorption
6.
We consider the Cauchy problem for the damped wave equation with absorption
(∗) 相似文献
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8.
Asymptotic profile of solutions for the damped wave equation with a nonlinear convection term 下载免费PDF全文
This paper is concerned with the large time behavior of solutions to the initial value problem for the damped wave equations with nonlinear convection in one‐dimensional whole space. In 2007, Ueda and Kawashima showed that the solution tends to a self similar solution of the Burgers equation. However, they did not mention that their decay estimate is optimal or not. Under this situation, the aim of this paper was to find out the sharp decay estimate by studying the second asymptotic profile of solutions. The explicit representation formula and the decay estimates of the solution for the linearized equation including the lower order term play crucial roles in our analysis. 相似文献
9.
Existence and orbital stability of periodic wave solutions for the nonlinear Schrodinger equation 下载免费PDF全文
Ai Yong Chen Shuangquan Wen Wentao Huang 《Journal of Applied Analysis & Computation》2012,2(2):137-148
In this paper, we study the existence and orbital stability of periodic wave solutions or the Schrödinger equation. The existence of periodic wave solution is obtained by using the phase portrait analytical technique. The stability approach is based on the theory developed by Angulo for periodic eigenvalue problems. A crucial condition of orbital stability of periodic wave solutions is proved by using qualitative theory of ordinal differential equations. The results presented in this paper improve the previous approach, because the proving approach does not dependent on complete elliptic integral of first kind and second kind. 相似文献
10.
M. Hamza 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(9):2897-2916
We consider the damped hyperbolic equation
(1) 相似文献
11.
结合齐次平衡法原理并利用F展开法,再次研究了Zhiber-Shabat方程的各种椭圆函数周期解.当椭圆函数的模m分别趋于1或0时,利用这些椭圆函数周期解,得到了Zhiber-Shabat方程的各种孤子解和三角函数周期解,从而丰富了相关文献中关于Zhiber-Shabat波方程的解的类型. 相似文献
12.
周盛凡 《应用数学学报(英文版)》2000,16(3):266-273
1. IntroductionConsider the strongly damped nonlinear wave equationwith the Dirichlet boundary conditionand the initial value conditionswhere u = u(x, t) is a real--valued function on fi x [0, co), fi is an open bounded set of R"with smooth boundary off, or > 0, g e L'(fl), D(--Q) ~ Ha(~~) n H'(fl).We assume for the function f(u) as follows'f(u) E CI (R, R) satisfiesfor any ig al, uZ E R, where k, hi > 0, i ~ 0, 1, 2, 61 > 0 and 0 5 6o < 1'The type of equation (1) can be regarded as the… 相似文献
13.
Bruno de Andrade Carlos Lizama 《Journal of Mathematical Analysis and Applications》2011,382(2):761-771
In this paper, a class of nonlinear damped wave equations of the form αu?(t)+u″(t)=βAu(t)+γAu′(t)+f(t,u(t)), t?0, satisfying αβ<γ with prescribed initial conditions are studied. Some sufficient conditions are established for the existence and uniqueness of an asymptotically almost periodic solution. These results have significance in the study of vibrations of flexible structures possessing internal material damping. Finally, an example is presented to illustrate the feasibility and effectiveness of the results. 相似文献
14.
Exact periodic wave solutions for the hKdV equation 总被引:1,自引:0,他引:1
In this paper, by using the Hirota bilinear method and the Jacobian theta functions for the higher order KdV equation, the existence of periodic wave solutions with one and two period are obtained. The asymptotic properties of the periodic wave solutions are analyzed in detail. It is shown that the well-known soliton solutions can be reduced from the periodic wave solutions. 相似文献
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16.
In this paper, for compound KdV equation, four new solitary wave solutions in the form of hyperbolic secant function and six periodic wave solutions in the form of cosine function are obtained by using undetermined coefficient method. On three different layers, the velocity interval which ensures that bell-shaped solitary wave solutions and periodic wave solutions exist synchronously is obtained, respectively. The length of the interval is related to coefficients of the two nonlinear terms. 相似文献
17.
In this paper, the Dullin-Gottwald-Holm equation is studied using semi-inverse method and integral bifurcation method. New periodic waves such as peakon-like periodic wave, compacton-like periodic wave and singular periodic wave are found and their dynamical behaviors and certain strange phenomena are explained using the proposed criterion. The exact parametric representations of these waves are also presented. 相似文献
18.
Quasi-periodic solutions for a nonlinear wave equation 总被引:4,自引:0,他引:4
Jürgen Pöschel 《Commentarii Mathematici Helvetici》1996,71(1):269-296
19.
In this work the existence of a global solution for the mixed problem associated to the nonlinear equation
20.
Bui An Ton 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(1):182-193
The existence of a time-periodic solution of a free boundary nonlinear wave equation in non cylindrical domains is established. The problem arises in the study of the identification of the coefficient of the wave equation and of the boundary of the region from the observed values of the solution in a fixed subregion. 相似文献
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