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A Toy Model of 4D Semilinear Weakly Hyperbolic Wave Equations

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Analysis, Probability, Applications, and Computation

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

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Abstract

In this chapter, we prove the large data almost global existence of the 4-dimensional weakly hyperbolic equation:

$$\displaystyle u_{tt}-(t_0-t)^2\varDelta u=-(t_0-t)^4|u|u\,. $$

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Acknowledgements

The Authors thank the anonymous referee for the available remarks. The first Author is grateful to the organizers of Special Interest Group IGPDE in the 11th ISAAC Congress at Linneuniversitetet in Sweden.

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Authors and Affiliations

  1. Department of Mathematics, University of Bari, Bari, Italy

    Sandra Lucente

  2. Dipartimento di Matematica, Università degli studi di Bari, Bari, Italy

    Emanuele Marrone

Authors
  1. Sandra Lucente
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  2. Emanuele Marrone
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Corresponding author

Correspondence to Sandra Lucente .

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Editors and Affiliations

  1. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Karl‐Olof Lindahl

  2. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Torsten Lindström

  3. Department of Mathematics, University of Torino, Torino, Italy

    Luigi G. Rodino

  4. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Joachim Toft

  5. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Patrik Wahlberg

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Lucente, S., Marrone, E. (2019). A Toy Model of 4D Semilinear Weakly Hyperbolic Wave Equations. In: Lindahl, K., Lindström, T., Rodino, L., Toft, J., Wahlberg, P. (eds) Analysis, Probability, Applications, and Computation. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-04459-6_33

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