Publication: Applications of cone structures to the anisotropic rheonomic Huygens’ principle
Authors
Javaloyes Victoria, Miguel Ángel ; Pendás-Recondo, Enrique ; Sánchez, Miguel
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Publisher
Elsevier
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DOI
https://doi.org/10.1016/j.na.2021.112337
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info:eu-repo/semantics/article
Description
© 2021 Elsevier Ltd. This document is the Published Manuscript, version of a Published Work that appeared in final form in Nonlinear Analysis. To access the final edited and published work see https://doi.org/10.1016/j.na.2021.112337
Abstract
A general framework for the description of classic wave propagation is introduced. This relies on a cone structure C determined by an intrinsic space Σ of velocities of propagation (point, direction and time-dependent) and an observers’ vector field ∂/∂t whose integral curves provide both a Zermelo problem for the wave and an auxiliary Lorentz–Finsler metric G compatible with C. The PDE for the wavefront is reduced to the ODE for the t-parametrized cone geodesics of C. Particular cases include time-independence (∂/∂t is Killing for G), infinitesimally ellipsoidal propagation (G can be replaced by a Lorentz metric) or the case of a medium which moves with respect to ∂/∂t faster than the wave (the “strong wind” case of a sound wave), where a conic time-dependent Finsler metric emerges. The specific case of wildfire propagation is revisited.
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Citation
Nonlinear Analysis, 2021, Vol. 209 : 112337
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