共查询到20条相似文献,搜索用时 288 毫秒
1.
Nakao Hayashi Pavel I. Naumkin Joel A. Rodriguez-Ceballos 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(3):355-369
We study large time asymptotic behavior of solutions to the periodic problem for the nonlinear damped wave equation
$ \left\{ {l} u_{tt}+2\alpha u_{t}-\beta u_{xx}=-\lambda \left| u\right| ^{\sigma}u,\text{ }x\in \Omega ,t >0 , \\ u(0,x)=\phi \left( x\right) ,\text{}u_{t}(0,x)=\psi \left( x\right) ,\text{ }x\in \Omega , \right. $ \left\{ \begin{array}{l} u_{tt}+2\alpha u_{t}-\beta u_{xx}=-\lambda \left| u\right| ^{\sigma}u,\text{ }x\in \Omega ,t >0 , \\ u(0,x)=\phi \left( x\right) ,\text{}u_{t}(0,x)=\psi \left( x\right) ,\text{ }x\in \Omega , \end{array} \right. 相似文献
2.
杜明笙 《应用数学学报(英文版)》1995,11(3):268-279
FINITEDIFFERENCESCHEMESOFTHENONLINEARPSEUDO-PARABOLICSYSTEMDUMINGSHENG(杜明笙)(InstituteofAppliedPhysicsandComputationalMathemat... 相似文献
3.
On the existence of full dimensional KAM torus for fractional nonlinear Schrodinger equation
![]() In this paper,\ we study fractional nonlinear Schrodinger equation (FNLS) with periodic boundary condition
$$
\textbf{i}u_{t}=-(-\Delta)^{s_{0}} u-V*u-\epsilon f(x)|u|^4u,\ ~~x\in \mathbb{T}, ~~t\in \mathbb{R}, ~~s_{0}\in (\frac12,1),~~~~~~~~~~~~~~~~~~~~~~~~~~~~(0.1)
$$
where $(-\Delta)^{s_{0}}$ is the Riesz fractional differentiation defined in [21] and $V*$ is the Fourier multiplier defined by $\widehat{V*u}(n)=V_n\widehat{u}(n),\ V_n\in\left[-1,1\right],$ and $f(x)$ is Gevrey smooth. We prove that for $0\leq|\epsilon|\ll1$ and appropriate $V$,\ the equation (0.1) admits a full dimensional KAM torus in the Gevrey space satisfying $ \frac12e^{-rn^{\theta}}\leq \left|q_n\right|\leq 2e^{-rn^{\theta}}, \theta\in (0,1),$
which generalizes the results given by [8-10] to fractional nonlinear Schrodinger equation. 相似文献
4.
In this paper, we consider the following nonlinear Kirchhoff wave equation
$\left\{\begin{array}{l}u_{tt}-\frac{\partial }{\partial x}(\mu (u,\Vert u_{x}\Vert ^{2})u_{x})=f(x,t,u,u_{x},u_{t}),\quad 0 where \(\widetilde{u}_{0}\), \(\widetilde{u}_{1}\), μ, f, g are given functions and \(\Vert u_{x}\Vert ^{2}=\int_{0}^{1}u_{x}^{2}(x,t)dx.\) To the problem (1), we associate a linear recursive scheme for which the existence of a local and unique weak solution is proved by applying the Faedo–Galerkin method and the weak compact method. In particular, motivated by the asymptotic expansion of a weak solution in only one, two or three small parameters in the researches before now, an asymptotic expansion of a weak solution in many small parameters appeared on both sides of (1)1 is studied.(1) 5.
6.
In this paper, we study the well-posedness of an initial-boundary-value problem (IBVP) for the Boussinesq equation on a bounded domain,\begin{cases} &u_{tt}-u_{xx}+(u^2)_{xx}+u_{xxxx}=0,\quad x\in (0,1), \;\;t>0,\\ &u(x,0)=\varphi(x),\;\;\; u_t(x,0)=ψ(x),\\ &u(0,t)=h_1(t),\;\;\;u(1,t)=h_2(t),\;\;\;u_{xx}(0,t)=h_3(t),\;\;\;u_{xx}(1,t)=h_4(t).\\ \end{cases} It is shown that the IBVP is locally well-posed in the space $H^s (0,1)$ for any $s\geq 0$ with the initial data $\varphi,$ $\psi$ lie in $H^s(0,1)$ and $ H^{s-2}(0,1)$, respectively, and the naturally compatible boundary data $h_1,$ $h_2$ in the space $H_{loc}^{(s+1)/2}(\mathbb{R}^+)$, and $h_3 $, $h_4$ in the the space of $H_{loc}^{(s-1)/2}(\mathbb{R}^+)$ with optimal regularity. 相似文献
7.
The induced matching cover number of a graph G without isolated vertices,denoted by imc(G),is the minimum integer k such that G has k induced matchings M1,M2,…,Mk such that,M1∪M2 ∪…∪Mk covers V(G).This paper shows if G is a nontrivial tree,then imc(G) ∈ {△*0(G),△*0(G) + 1,△*0(G)+2},where △*0(G) = max{d0(u) + d0(v) :u,v ∈ V(G),uv ∈ E(G)}. 相似文献
8.
The initial boundary value problem
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