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Speed of wave-front solutions to hyperbolic reaction-diffusion equations

The asymptotic speed problem of front solutions to hyperbolic reaction-diffusion (HRD) equations is studied in detail. We perform linear and variational analyses to obtain bounds for the speed. In contrast to what has been done in previous work, here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds. For some functions it is possible to determine the speed without any uncertainty. This is also achieved for some systems of HRD (i.e., time-delayed Lotka-Volterra) equations that take into account the interaction among different species. An analytical analysis is performed for several systems of biological interest, and we find good agreement with the results of numerical simulations as well as with available observations for a system discussed recently

© Physical Review E, 1999, vol. 60, núm. 5, p. 5231-5243

American Physical Society

Author: Méndez López, Vicenç
Fort, Joaquim
Farjas Silva, Jordi
Date: 1999
Abstract: The asymptotic speed problem of front solutions to hyperbolic reaction-diffusion (HRD) equations is studied in detail. We perform linear and variational analyses to obtain bounds for the speed. In contrast to what has been done in previous work, here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds. For some functions it is possible to determine the speed without any uncertainty. This is also achieved for some systems of HRD (i.e., time-delayed Lotka-Volterra) equations that take into account the interaction among different species. An analytical analysis is performed for several systems of biological interest, and we find good agreement with the results of numerical simulations as well as with available observations for a system discussed recently
Format: application/pdf
ISSN: 1539-3755 (versió paper)
1550-2376 (versió electrònica)
Document access: http://hdl.handle.net/10256/7708
Language: eng
Publisher: American Physical Society
Collection: Reproducció digital del document publicat a: http://link.aps.org/doi/10.1103/PhysRevE.60.5231
Articles publicats (D-F)
Is part of: © Physical Review E, 1999, vol. 60, núm. 5, p. 5231-5243
Rights: Tots els drets reservats
Subject: Equacions de reacció-difusió
Reaction-diffusion equations
Equacions diferencials hiperbòliques
Differential equations, Hyperbolic
Models matemàtics
Mathematical models
Title: Speed of wave-front solutions to hyperbolic reaction-diffusion equations
Type: info:eu-repo/semantics/article
Repository: DUGiDocs

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