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Self-similar Asymptotic Profile for a Damped Evolution Equation

  • Marcello D’Abbicco
Conference paper
Part of the Trends in Mathematics book series (TM)

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.

Notes

Acknowledgements

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

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Marcello D’Abbicco
    • 1
  1. 1.Department of MathematicsUniversity of BariBariItaly

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