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Well-Posedness for a Generalized Boussinesq Equation

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Book cover Current Trends in Analysis and Its Applications

Part of the book series: Trends in Mathematics ((RESPERSP))

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Abstract

We consider a generalization of the Boussinesq equation obtained by adding a term of the form \(a(t,x,u)\partial_{x}^{3}u\). We prove local in time well-posedness of the Cauchy problem in Sobolev spaces under a suitable decay condition on the real part of the coefficient a(t,x,u), as x→∞.

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References

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica ed Informatica, Università di Ferrara, Via Machiavelli n. 35, 44121, Ferrara, Italy

    Alessia Ascanelli & Chiara Boiti

Authors
  1. Alessia Ascanelli
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  2. Chiara Boiti
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Corresponding author

Correspondence to Alessia Ascanelli .

Editor information

Editors and Affiliations

  1. Dept. of Computer Sc. & Comp. Methods, Pedagogical University, Kraków, Poland

    Vladimir V. Mityushev

  2. Imperial College London, London, United Kingdom

    Michael V. Ruzhansky

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Ascanelli, A., Boiti, C. (2015). Well-Posedness for a Generalized Boussinesq Equation. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_23

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