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Convergence of the regularized short pulse equation to the short pulse one

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  • Giuseppe Maria Coclite
  • Lorenzo di Ruvo

Abstract

We consider the regularized short†pulse equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the short†pulse one. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the Lp setting.

Suggested Citation

  • Giuseppe Maria Coclite & Lorenzo di Ruvo, 2018. "Convergence of the regularized short pulse equation to the short pulse one," Mathematische Nachrichten, Wiley Blackwell, vol. 291(5-6), pages 774-792, April.
    • Handle: RePEc:bla:mathna:v:291:y:2018:i:5-6:p:774-792
    DOI: 10.1002/mana.201600301
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    Cited by:

    1. Giuseppe Maria Coclite & Lorenzo Ruvo, 2022. "On the initial-boundary value problem for a non-local elliptic-hyperbolic system related to the short pulse equation," Partial Differential Equations and Applications, Springer, vol. 3(6), pages 1-40, December.
    2. Giuseppe Maria Coclite & Lorenzo di Ruvo, 2019. "Well-Posedness Results for the Continuum Spectrum Pulse Equation," Mathematics, MDPI, vol. 7(11), pages 1-39, October.
    3. Giuseppe Maria Coclite & Lorenzo di Ruvo, 2020. "A Note on the Solutions for a Higher-Order Convective Cahn–Hilliard-Type Equation," Mathematics, MDPI, vol. 8(10), pages 1-31, October.

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