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Asymptotic Behavior of the Subordinated Traveling Waves

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Abstract

In this paper we investigate the long-time behavior of the subordination of the constant speed traveling waves by a general class of kernels. We use the Feller–Karamata Tauberian theorem in order to study the long-time behavior of the upper and lower wave. As a result we obtain the long-time behavior for the propagation of the front of the wave.

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Acknowledgements

This work has been partially supported by Center for Research in Mathematics and Applications (CIMA) related with the Statistics, Stochastic Processes and Applications (SSPA) group, through the Grant UIDB/MAT/04674/2020 of FCT-Fundação para a Ciência e a Tecnologia, Portugal. The financial support by the Ministry for Science and Education of Ukraine through Project 0119U002583 is gratefully acknowledged. Finally, we would like to thank the anonymous referee for pointing out some misprints and comments which improves the overall quality of the paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Bielefeld, 33615, Bielefeld, Germany

    Yuri Kondratiev

  2. Dragomanov University, Kiev, Ukraine

    Yuri Kondratiev

  3. CIMA, University of Madeira, Campus da Penteada, 9020-105, Funchal, Portugal

    José Luís da Silva

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  1. Yuri Kondratiev
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  2. José Luís da Silva
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Correspondence to José Luís da Silva.

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Communicated by Clement Mouhot.

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The first author is supported by the Ministry for Science and Education of Ukraine Grant 0119U002583 and the second by the Fundação para a Ciência e a Tecnologia, Portugal grant UIDB/MAT/04674/2020.

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Kondratiev, Y., Silva, J.L.d. Asymptotic Behavior of the Subordinated Traveling Waves. J Stat Phys 183, 7 (2021). https://doi.org/10.1007/s10955-021-02745-x

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