Spectral approach to homogenization of hyperbolic equations with periodic coefficients
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DOI: 10.1016/j.jde.2018.02.023
Abstract: In $L_2(\mathbb{R}^d;\mathbb{C}^n)$, we consider selfadjoint strongly elliptic second order differential operators ${\mathcal A}_\varepsilon$ with periodic coefficients depending on ${\mathbf x}/ \varepsilon$, $\varepsilon>0$. We study the behavior of the operators $\cos( {\mathcal A}^{1/2}_\varepsilon \tau)$ and ${\mathcal… read more here.
Keywords: periodic coefficients; tau; varepsilon; mathcal varepsilon ... See more keywords
NLS approximation for wavepackets in periodic cubically nonlinear wave problems in ℝd
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DOI: 10.1080/00036811.2018.1544620
Abstract: ABSTRACT The dynamics of single carrier wavepackets in nonlinear wave problems over periodic structures can be often formally approximated by the constant coefficient nonlinear Schrödinger equation as an effective model for the wavepacket envelope. We… read more here.
Keywords: periodic coefficients; approximation; nls approximation; approximation wavepackets ... See more keywords
Estimates for Solutions to Neutral Differential Equations with Periodic Coefficients of Linear Terms
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DOI: 10.1134/s0037446619050069
Abstract: Under study are the systems of nonlinear delay differential equations of neutral type with periodic coefficients of linear terms. We establish sufficient conditions of exponential stability of the zero solution, point out the attraction domains… read more here.
Keywords: periodic coefficients; linear terms; estimates solutions; solutions neutral ... See more keywords