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Hierarchic Control for the Wave Equation
Journal of Optimization Theory and Applications, 2018The paper deals with the hierarchical control of the wave equation. The authors consider a problem setting with one leader and two followers. Both the linear and semilinear equations are considered, the latter with a globally Lipschitz nonlinear term. For the linear equation the main result of the paper consists in obtaining the existence of a leader ...
Fágner D. Araruna +2 more
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Wave equation receiver deghosting
2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2013Current solutions to receiver deghosting generally involve making complementary measurements of the wavefield or, alternatively, involve estimation of data not recorded due to ghost interference. Both solutions offer challenges in practice today. For marine streamer data, although multimeasurement streamers are commercially available, it is still on a ...
Craig J. Beasley +2 more
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2008
These notes give an overview of recent results concerning the non-linear stochastic wave equation in spatial dimensions d >= 1, in the case where the driving noise is Gaussian, spatially homogeneous and white in time. We mainly address issues of existence, uniqueness and Holder-Sobolev regularity.
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These notes give an overview of recent results concerning the non-linear stochastic wave equation in spatial dimensions d >= 1, in the case where the driving noise is Gaussian, spatially homogeneous and white in time. We mainly address issues of existence, uniqueness and Holder-Sobolev regularity.
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The Wave Equation in a Medium in Motion
IBM Journal of Research and Development, 1960A model for the transverse vibrations of a tape moving between a pair of pulleys is devised using a variational procedure. It is shown by means of energy-type integrals that the energy of that portion of the tape between the pulleys is not conserved, but that there is a periodic transfer of energy into and out of the system.
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The nonlinear wave equation as a Liénard equation
Funkcialaj Ekvacioj, 1991In the study of the asymptotic behavior of solutions to the equation \[ u_{tt}+f(u)u_t+g(u)=0, \] where \(f,g\in C^0\), \(f(u)>0\) and \(ug(u)>0\) for \(u\neq 0\), much of the investigation was carried out by means of Lyapunov's direct method and the natural Lyapunov function for the equation is \(V_1(t):= 2\int_0^u g(s)\,ds+u_t^2\).
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2021
In this chapter, partial differential equations that govern many featured wave propagation phenomena are discussed. We start with modelling the process of string vibration through a partial differential equation, known as the wave equation, or the equation for string vibration. Then the concepts of initial and boundary conditions are introduced.
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In this chapter, partial differential equations that govern many featured wave propagation phenomena are discussed. We start with modelling the process of string vibration through a partial differential equation, known as the wave equation, or the equation for string vibration. Then the concepts of initial and boundary conditions are introduced.
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PINN deep learning method for the Chen–Lee–Liu equation: Rogue wave on the periodic background
Communications in Nonlinear Science and Numerical Simulation, 2022Yong Chen
exaly