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1.
The three-dimensional equations of compressible magnetohydrodynamic isentropic flows are considered. An initial-boundary value
problem is studied in a bounded domain with large data. The existence and large-time behavior of global weak solutions are
established through a three-level approximation, energy estimates, and weak convergence for the adiabatic exponent ${\gamma > \frac 32}${\gamma > \frac 32} and constant viscosity coefficients. 相似文献
2.
The Navier-Stokes equation for compressible viscous fluid is considered on the half space in R
3 under the zero-Dirichlet boundary condition for the momentum with initial data near an arbitrarily given equilibrium of positive
constant density and zero momentum. Time decay properties in L
2 norms for solutions of the linearized problem are investigated to obtain the rate of convergence in L
2 norms of solutions to the equilibrium when initial data are sufficiently close to the equilibrium in . Some lower bounds are derived for solutions to the linearized problem, one of which indicates a nonlinear phenomenon not
appearing in the case of the Cauchy problem on the whole space.
(Accepted May 8, 2002) Published online October 18, 2002
Communicated by T.-P. LIU 相似文献
3.
4.
Renato C. Calleja Alessandra Celletti Rafael de la Llave 《Journal of Dynamics and Differential Equations》2013,25(3):821-841
We study the behaviour of conformally symplectic systems near rotational Lagrangian tori. We recall that conformally symplectic systems appear for example in mechanical models including a friction proportional to the velocity. We show that in a neighborhood of these Lagrangian, invariant, rotational tori, one can always find a smooth symplectic change of variables in which the time evolution becomes just a rotation in some direction and a linear contraction in others. In particular quasi-periodic solutions with $n$ n independent frequencies of contractive (expansive) diffeomorphisms are always local attractors (repellors). We present results when the systems are analytic, $C^r$ C r or $C^\infty $ C ∞ . We emphasize that the results presented here are non-perturbative and apply to systems that are far from integrable; moreover, we do not require any assumption on the frequency and in particular we do not assume any non-resonance condition. We also show that the system of coordinates can be computed rather explicitly and we provide iterative algorithms, which allow to generalize the notion of “isochrones”. We conclude by showing that the above results apply to quasi-periodic conformally symplectic flows. 相似文献
5.
The three-dimensional equations for the compressible flow of liquid crystals are considered. An initial-boundary value problem
is studied in a bounded domain with large data. The existence and large-time behavior of a global weak solution are established
through a three-level approximation, energy estimates, and weak convergence for the adiabatic exponent ${\gamma > \frac{3}{2}}${\gamma > \frac{3}{2}} . 相似文献
6.
This paper is concerned with the large-time behaviour of energy for the n-dimensional nonhomogeneous and anisotropic elastic system with a locally reacting boundary subject to small oscillations. Under reasonable assumptions, the polynomial decay for the energy of such a model has been established. Multiplicative techniques and the energy method are used. 相似文献
7.
Consider a strictly hyperbolic system of conservation laws in one space dimension: Relying on the existence of the Standard Riemann Semigroup generated by , we establish the uniqueness of entropy-admissible weak solutions to the Cauchy problem, under a mild assumption on the variation of along space-like segments. 相似文献
8.
城市高架桥车-桥-墩系统竖向振动分析 总被引:1,自引:0,他引:1
假设城市高架桥为两端简支的欧拉-伯努利梁模型以及桥墩为底部固结的柱,考虑两自由度车辆移动系统与桥面结构表面接触处不平整产生的随机激励以,建立了多个移动车辆系统-桥-墩的耦合力学模型,并且给出了耦合振动方程详细的求解步骤.数值分析采用Wilson-θ法求解.通过仿真分析,讨论了在不同路面等级、不同车辆移动速度下桥梁跨中位移响应和桥墩轴力的变化规律.最后根据车-桥-墩耦合力学模型和车-桥耦合力学模型,比较了两种分析模型对桥墩底部轴力和桥梁跨中截面位移的影响.分析结果表明桥墩对桥梁跨中截面位移的影响可以忽略不计,但是对桥墩本身所受轴力的影响则非常显著. 相似文献
9.
?We estimate the Hausdorff dimension of the singular set of solutions to elliptic systems of the type
If the vector fields a and b are Hölder continuous with respect to the variable x with exponent α, then the Hausdorff dimension of the singular set of any weak solution is at most n?2α.
相似文献10.
11.
We consider here a model of fluid-structure evolution
problem which, in particular, has been largely studied from the
numerical point of view. We prove the existence of a strong
solution to this problem. 相似文献
12.
. We give an intrinsic definition of a heteroclinic network as a flow-invariant set that is indecomposable but not recurrent.
Our definition covers many previously discussed examples of heteroclinic behavior. In addition, it provides a natural framework
for discussing cycles between invariant sets more complicated than equilibria or limit cycles. We allow for cycles that connect
chaotic sets (cycling chaos) or heteroclinic cycles (cycling cycles). Both phenomena can occur robustly in systems with symmetry.
We analyze the structure of a heteroclinic network as well as dynamics on and near the network. In particular, we introduce
a notion of ‘depth’ for a heteroclinic network (simple cycles between equilibria have depth 1), characterize the connections
and discuss issues of attraction, robustness and asymptotic behavior near a network.
We consider in detail a system of nine coupled cells where one can find a variety of complicated, yet robust, dynamics in
simple polynomial vector fields that possess symmetries. For this model system, we find and prove the existence of depth‐2
networks involving connections between heteroclinic cycles and equilibria, and study bifurcations of such structures.
(Accepted July 6, 1998) 相似文献
13.
We consider the system Δu ? W u (u) = 0, where \({u : \mathbb{R}^n \to \mathbb{R}^n}\) , for a class of potentials \({W : \mathbb{R}^n \to \mathbb{R}}\) that possess several global minima and are invariant under a general finite reflection group G. We establish existence of nontrivial G-equivariant entire solutions connecting the global minima of W along certain directions at infinity. 相似文献
14.
Takayuki Kobayashi Takashi Suzuki Kazuo Watanabe 《Journal of Mathematical Fluid Mechanics》2006,8(3):382-397
This paper is concerned with the component-wise regularity of the solution to the stationary Maxwell or Stokes systems. We
assume that there is a surface
in R3, regarded as an interface, and the solution u to one of the systems is smooth except for this
. Then, under these assumptions, we can show that some components of u are smooth across
. In the Maxwell system, the normal component of u is always regular across
. On the other hand, in the Stokes system, the singularity of u across
can only arise to the normal derivatives of its tangential components. Furthermore, these results are shown to be optimal. 相似文献
15.
In this paper, by linking Fokker–Planck equations with stochastic coupled systems, a new method is provided to investigate the existence of a stationary distribution of stochastic coupled systems. Based on the graph theory and the Lyapunov method, an appropriate Lyapunov function associated with stationary Fokker–Planck equations is constructed. Moreover, a Lyapunov-type theorem and a coefficients-type criterion are obtained to guarantee the existence of a stationary distribution. Furthermore, theoretical results are applied to explore the existence of a stationary distribution of stochastic predator–prey models with dispersal and a sufficient criterion is presented correspondingly. Finally, a numerical example is given to illustrate the effectiveness of our results. 相似文献
16.
A two degrees of freedom model of two coupled suspension systems characterised by piecewise linear stiffness has been studied. The system, representing a pantograph current collector head, is shown to be sensitive to changes in excitation and system parameters, possessing chaotic, periodic and quasiperiodic behaviour. The coupled system has a more irregular behaviour with larger motions than the uncoupled suspension system, indicating that the response from the uncoupled suspension system cannot be used as a worst case measure. Since small changes in system parameters and excitation affect the results drastically then wear and mounting as well as actual operating conditions are crucial factors for the system behaviour. 相似文献
17.
Archive for Rational Mechanics and Analysis - In the present work we introduce the notion of a renormalized solution for reaction–diffusion systems with entropy-dissipating reactions. We... 相似文献
18.
Species concentrations in homogeneous well-stirred reacting (WSR) systems with multiple time scales mostly access only a small portion (slow manifold) of the permitted composition space. This offers a mathematically sound basis for reducing complex kinetics. Computational investigation of such slow manifolds in inhomogeneous reaction systems undergoing diffusion in addition to chemical reaction is the subject of this paper. We perform simulations of a one-dimensional diffusion–reaction system from random non-premixed initial conditions to study the accessed composition space for a variety of diffusion to reaction time scale ratios. A detailed hydrogen–oxygen chemical kinetic set (6 species, 14 reactions) is used. Our results show that, to first order, the effect of random advection and diffusion is merely to increase the accessed state-space dimensionality over that of the WSR by the number of relevant mixture fractions. Circumstances under which the above simplification is not accurate are also identified. 相似文献
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