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Networks and Heterogeneous Media

2016, Volume 11, Issue 3: 369-393. doi: 10.3934/nhm.2016001
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Varying the direction of propagation in reaction-diffusion equations in periodic media

  • 1.
    IMAG, CC051, Université de Montpellier , 34095 Montpellier
  • 2.
    IECL, Université de Lorraine, B.P. 70239, 54506 Vandoeuvre-lès-Nancy Cedex
  • Received: 01 February 2015 Revised: 01 February 2016

  • Primary: 35K57; Secondary: 35B10.

  • We consider a multidimensional reaction-diffusion equation of either ignition or monostable type, involving periodic heterogeneity, and analyze the dependence of the propagation phenomena on the direction. We prove that the (minimal) speed of the underlying pulsating fronts depends continuously on the direction of propagation, and so does its associated profile provided it is unique up to time shifts. We also prove that the spreading properties [25] are actually uniform with respect to the direction.

    Citation: Matthieu Alfaro, Thomas Giletti. Varying the direction of propagation in reaction-diffusion equations in periodic media[J]. Networks and Heterogeneous Media, 2016, 11(3): 369-393. doi: 10.3934/nhm.2016001

    Related Papers:

  • We consider a multidimensional reaction-diffusion equation of either ignition or monostable type, involving periodic heterogeneity, and analyze the dependence of the propagation phenomena on the direction. We prove that the (minimal) speed of the underlying pulsating fronts depends continuously on the direction of propagation, and so does its associated profile provided it is unique up to time shifts. We also prove that the spreading properties [25] are actually uniform with respect to the direction.


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    9. Weiwei Ding, François Hamel, Xing Liang, Bistable pulsating fronts in slowly oscillating one-dimensional environments, 2025, 00217824, 103668, 10.1016/j.matpur.2025.103668
    10. Suobing Zhang, Zhi-Cheng Wang, Fu-Jie Jia, Transition Fronts of Combustion Reaction Diffusion Equations in Spatially Periodic Media, 2025, 35, 1050-6926, 10.1007/s12220-025-01947-z
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