1-D discretized wave equation
Uniform observability estimates for the 1-D discretized wave equation and the random choice method
... Ces deux ´ equations sont des cas tr` es particuliers de syst` emes de lois de conservation unidimensionnels pour lesquelles J. Glimm a obtenu un r´ esultat tr` es g´ en´ eral d’existence de solutions au moyen d’un al- ...
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Artificial boundary conditions for the semi-discretized one-dimensional nonlocal Schrödinger equation
... ik(x−kt)− (x−2kt)2 4(ζ+it) , (55) with ζ = 0.04 and wave number k = 2. The spatial computational domain is [−3, 3] and the final time is T = 0.2. We fix a very small time step ∆t = 10 −5 and vary the spatial ...
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Pointwise moving control for the 1-D wave equation - Numerical approximation and optimization of the support
... Fig. 8: (Ex4.1) – Initial trajectory 𝛾 0 , optimal trajectory 𝛾 ⋆ and optimal controlled state 𝜆 ⋆ (from left to right). and time variables, making it very appropriate to our moving point situation. We have shown the ...
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Efficient solution of a wave equation with fractional-order dissipative terms
... its discretized versions a fractional integral for the internal damping, together with more realistic boundary conditions of the impedance type, thus introducing some external damping, as was done in [ 6 ...
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Control of a Wave Equation with a Dynamic Boundary Condition
... Figures 1 and 2 are obtained with the following parameters: we take α = 1, F (x) = qx with q = ...= 1. The domain Ω is discretized into 100 points and the time step is set to ...
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THREE LONG WAVE ASYMPTOTIC REGIMES FOR THE NONLINEAR SCHRODINGER EQUATION.
... = 1 and in the integrable cases for (NLS), this problem has also been studied: for f (̺) = ̺ and f (̺) = ̺ − 1 in [39], and in the focusing case f (̺) = −̺ by ...
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EIGENMODES OF THE DAMPED WAVE EQUATION AND SMALL HYPERBOLIC SUBSETS
... properties of (1) have been obtained by various authors. For instance, in a very general context, Lebeau related the geometry of the undamped geodesics, the spectral asymptotics of the τ n and the energy decay of ...
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Dispersion for the wave equation outside a ball and counterexamples
... Schr¨odinger equation, the dispersive estimates read as follows: ke ±it∆ Rd k L 1 (R d )→L ∞ (R d ) ≤ C(d)|t| −d/2 ...refocus wave packets), one would expect dispersive estimates to hold outside ...
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PI controllers for 1-D nonlinear transport equation
... transport equation with a PI boundary controller which was studied in [24], and in which the authors obtained a sufficient, although conservative, stability ...this equation interesting in itself [8] but it ...
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Asymptotics of Solutions of the Wave Equation on de Sitter-Schwarzschild Space
... R(σ) = (∆ X − σ 2 ) −1 , Im σ < 0. Here we also need high-energy estimates for R(σ). The operator ∆ X has been studied by the second author and Zworski in [9], where it is shown (using the spherical symmetry to ...
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Numerical resolution of the wave equation on a network of slots
... [6] Patrick Joly and Adrien Semin. Propagation of an acoustic wave in a junction of two thin slots. Research Report RR-6708, INRIA, October 2008. [7] Patrick Joly and Adrien Semin. Construction and Analysis of ...
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Asymptotics of the solutions of the stochastic lattice wave equation
... When the interaction is linear, the thermal diffusivity of the energy in these models can be explicitly computed – it is finite for the pinned model but diverges with the size of the system in the unpinned case ...
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A minimum effort optimal control problem for the wave equation.
... differential equation are developed in publications, see, ...the wave equa- tion is significantly less rich than for that for equations of parabolic ...
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On the convergence of the fictitious domain method for wave equation problems
... incident wave is completely reflected by the obstacle and the scattered waves generated by the extremities of the crack are well approximated (see figure ...
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A novel generalized dispersion equation to design circumferential wave fluid sensors
... torsional) wave propagation in long anisotropic cylindrical rod (waveguide), surrounded by a viscoelastic fluid is ...dispersion equation is ...the wave characteristics (phase and ...the wave ...
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An Analysis of Higher Order Boundary Conditions for the Wave Equation.
... Unité de recherche INRIA Rocquencourt Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex France Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois -[r] ...
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AN ANALYSIS OF HIGHER ORDER BOUNDARY CONDITIONS FOR THE WAVE EQUATION
... other wave equations) of the Engquist–Majda ...any wave propagating in the computational domain is transmitted to the absorbing layer without being ...
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A note on the global controllability of the semilinear wave equation
... nonlinear wave equations (see [33] for example). Of course, our proof of Theorem 1 is not really constructive, because the computation of heteroclinic orbits is not ...Theorem 1 gives an explicit way ...
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Characterization of Bijective Discretized Rotations
... L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignemen[r] ...
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Exponential decay for the damped wave equation in unbounded domains
... H 1 ,→ L 2p for p < d/(d − 2) or to more technical arguments based on the Strichartz estimates for p ∈ [d/(d − 2), (d + 2)/(d − 2)) (see [9] and see ...H 1 (R d ) × L 2 (R d ) for all t ∈ R (as ...
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