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Self-similar Asymptotic Profile for a Damped Evolution Equation

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Analysis, Probability, Applications, and Computation

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

Abstract

In this note, we describe the self-similar asymptotic profile for evolution equations with strong, effective damping. We assume that initial data are in weighted Sobolev spaces, and the second data verifies suitable moment conditions. The asymptotic profile is obtained by means of the application of a differential operator given by a linear combination of Riesz potentials to the fundamental solution of a (polyharmonic) diffusive problem.

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Acknowledgements

The author has been supported by the INdAM—GNAMPA Project 2017 Equazioni di tipo dispersivo e proprietà asintotiche.

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Authors and Affiliations

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

    Marcello D’Abbicco

Authors
  1. Marcello D’Abbicco
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Editor information

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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D’Abbicco, M. (2019). Self-similar Asymptotic Profile for a Damped Evolution Equation. 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_28

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