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Wave features of a hyperbolic reaction–diffusion model for Chemotaxis
Institution:1. Department of Mathematical, Computer, Physical and Earth Sciences, University of Messina, V.le F. Stagno D’Alcontres 31, Messina I-98166, Italy;2. Department of Engineering, University of Messina, C. Di Dio, Messina I-98166, Italy;1. Institute of General Mechanics, RWTH Aachen University, Templergraben 64, 52062 Aachen, Germany;2. School of Computing and Mathematics, Keele University, Staffordshire, ST5 5BG, UK;3. Carnegie Mellon University in Qatar, P.O. Box 24866, Doha, Qatar;4. Center for Advanced Materials, Qatar University, P.O. Box 2713, Doha, Qatar;1. Department of Mathematical Engineering, Y?ld?z Technical University, Davutpa?a, Istanbul, Turkey;2. Department of Mathematics, Marmara University, Kadiköy, Istanbul, Turkey;1. University College London, UK;2. School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, The King’s Buildings, Peter Guthrie Tait Road, Edinburgh, Scotland, EH9 3FD, UK;3. Faculty of Health, Engineering and Sciences, University of Southern Queensland, Toowoomba, QLD, 4350, Australia;4. Department of Applied Mathematics, Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Nizhny Novgorod, Russia
Abstract:The Extended Thermodynamic theory is used to derive a hyperbolic reaction–diffusion model for Chemotaxis. Linear stability analysis is performed to study the nature of the equilibrium states against uniform and nonuniform perturbations. A particular emphasis is given to the occurrence of the Turing bifurcation. The existence of traveling wave solutions connecting the two steady states is investigated and the governing equations are numerically integrated to validate the analytical results. The propagation of plane harmonic waves is analyzed and the stability regions in terms of the model parameters are shown. The frequency dependence of the phase velocity and of the attenuation is also illustrated. Finally, in order to have a measure of the non linear stability, the propagation of acceleration waves is studied, the wave amplitude is derived and the critical time is evaluated.
Keywords:Hyperbolic reaction–diffusion model  Traveling wave solutions  Extended Thermodynamics theory  Nonlinear waves  Turing bifurcation
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