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Phase Plane Behavior of Solitary Waves in Nonlinear Layered Media

LeVeque, Randall J. and Yong, Darryl H. (2003) Phase Plane Behavior of Solitary Waves in Nonlinear Layered Media. In: Hyperbolic Problems: Theory, Numerics, Applications. Springer , Berlin, pp. 43-51. ISBN 978-3-642-62929-7.

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The one-dimensional elastic wave equations for compressional waves have the form ∈_t(x,t)−u_x(x,t) = 0 (ρ(x)u(x,t))_t−σ(∈(x,t),x)_x = 0 (1)where ε(x, t) is the strain and u(x, t) the velocity. We consider a heterogeneous material with the density specified by ρ(x) and a nonlinear constitutive relation for the stress given by a function σ(∈, x) that also varies explicitly with x. This is a hyperbolic system of conservation laws with a spatially-varying flux function, q_t + f(q, x)_x = 0.

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Additional Information:© 2003 Springer-Verlag Berlin Heidelberg. This work was supported in part by DOE grant DE-FG03-96ER25292 and NSF grants DMS-9803442 and DMS-0106511.
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG03-96ER25292
Subject Keywords:Solitary Wave; Finite Volume Method; Hyperbolic System; Wave Train; Integral Curve
Record Number:CaltechAUTHORS:20200106-102812902
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100528
Deposited By: Tony Diaz
Deposited On:08 Jan 2020 19:57
Last Modified:16 Nov 2021 17:54

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