In this chapter, we study the control problem of the linear wave equation $$\\\frac{\\\partial^2 u}{\\\partial t^2} = c^2 abla^2 u.$$ This equation can serve as a mathematical model for many physical problems, such as the vibration of a membrane. In the membrane problem, u ...
In this chapter, we study the control problem of the one-dimensional wave equation $$\frac{\partial^2 u}{\partial t^{2}} = c^2 \frac{\partial^2 u}{\partial x^2}.$$ A typical physical problem modeled by the wave equation is the vibration of a string. In this problem, u = u...
1) one dimensional wave equation 一维波波动方程式1. This paper is to study how the lengths of foundation piles influencing driven piles by one dimensional wave equation. 应用一维波波动方程式探讨基桩长度对打击桩的影响。2) one-dimensional wave equation 一维波动方程 1. Long-term stability of ...
wave equations/ parameter estimationparameter stabilisationWe are concerned with the parameter estimation and stabilisation of a one-dimensional wave equation with an unknown constant disturbance suffered by boundary observation at one end and the non-collocated control at another end. An adaptive observer...
Firstly,thetestingprinciplewithaxial precompressionstressis re-examined basedonone-dimensionalwavetheory. 首先按照一维应力波传播理论,对动静组合加载的试验原理进行理论论证。 www.rockmech.org 3. TheBestPerturbationMethodfor theParameterInverseProblemofOneDimensionalWaveEquation ...
1) one-dimensional wave equation 一维波动方程 1. Long-term stability of solutions to theone-dimensional wave equation; 一维波动方程的解的长期稳定性 2. Oscillation ofone-dimensional wave equationand heat diffusion equation under certain fixed solution conditions is discussed in this paper. ...
p acement process has been simu ated and a simp ified formu a for the rep acement depth estimation is presented. Key words:dynamic rep acement;rep acement depth;one-dimensiona wave mode ;parameter;simp ified for- mu a. 9 1 1 第1 期 罗嗣海等:置换深度估算的一维波动方程法相关...
We present a method for two-scale model derivation of the periodic homogenization of the one-dimensional wave equation in a bounded domain. It allows for analyzing the oscillations occurring on both microscopic and macroscopic scales. The novelty reported here is on the asymptotic behavior of high ...
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We discuss the Cauchy problem for a one-dimensional wave equation with white noise boundary condition. We also establish the existence of an invariant measure when the noise is additive. Similar problems for parabolic equations were discussed by several authors. To our knowledge, there is only one...