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On the existence of chaos for the viscous van Wijngaarden–Eringen equation

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  • Conejero, J. Alberto
  • Lizama, Carlos
  • Murillo-Arcila, Marina

Abstract

We study the viscous van Wijngaarden–Eringen equation: (1)∂2u∂t2−∂2u∂x2=(Red)−1∂3u∂t∂x2+a02∂4u∂t2∂x2which corresponds to the linearized version of the equation that models the acoustic planar propagation in bubbly liquids. We show the existence of an explicit range, solely in terms of the constants a0 and Red, in which we can ensure that this equation admits a uniformly continuous, Devaney chaotic and topologically mixing semigroup on Herzog’s type Banach spaces.

Suggested Citation

  • Conejero, J. Alberto & Lizama, Carlos & Murillo-Arcila, Marina, 2016. "On the existence of chaos for the viscous van Wijngaarden–Eringen equation," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 100-104.
    • Handle: RePEc:eee:chsofr:v:89:y:2016:i:c:p:100-104
    DOI: 10.1016/j.chaos.2015.10.009
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    References listed on IDEAS

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    1. Xavier Barrachina & J. Alberto Conejero, 2012. "Devaney Chaos and Distributional Chaos in the Solution of Certain Partial Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-11, December.
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    Cited by:

    1. Lizama, Carlos & Murillo-Arcila, Marina, 2023. "On the existence of chaos for the fourth-order Moore–Gibson–Thompson equation," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).

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