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Trends in Control Theory and Partial Differential Equations pp 157–180Cite as

A Semilinear Integro-Differential Equation: Global Existence and Hidden Regularity

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Part of the book series: Springer INdAM Series ((SINDAMS,volume 32))

Abstract

Here we show a hidden regularity result for nonlinear wave equations with an integral term of convolution type and Dirichlet boundary conditions. Under general assumptions on the nonlinear term and on the integral kernel we are able to state results about global existence of strong and mild solutions without any further smallness on the initial data. Then we define the trace of the normal derivative of the solution showing a regularity result. In such a way we extend to integrodifferential equations with nonlinear term well-known results available in the literature for linear wave equations with memory.

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Acknowledgements

The authors would like to thank the anonymous referee for helpful comments improving the presentation of the paper.

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Authors and Affiliations

  1. Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza Università di Roma, Via Antonio Scarpa 16, 00161, Rome, Italy

    Paola Loreti & Daniela Sforza

Authors
  1. Paola Loreti
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  2. Daniela Sforza
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Corresponding author

Correspondence to Daniela Sforza .

Editor information

Editors and Affiliations

  1. Laboratoire Jacques-Louis Lions UMR 7598, Sorbonne Université, Paris, France

    Fatiha Alabau-Boussouira

  2. Dipartimento di Matematica “Tullio Levi-Civita”, Università degli Studi di Padova, Padua, Italy

    Fabio Ancona

  3. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Rome, Italy

    Alessio Porretta

  4. Dipartimento di Ingegneria Civile e Ingegneria Informatica, Università di Roma “Tor Vergata”, Rome, Italy

    Carlo Sinestrari

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Loreti, P., Sforza, D. (2019). A Semilinear Integro-Differential Equation: Global Existence and Hidden Regularity. In: Alabau-Boussouira, F., Ancona, F., Porretta, A., Sinestrari, C. (eds) Trends in Control Theory and Partial Differential Equations. Springer INdAM Series, vol 32. Springer, Cham. https://doi.org/10.1007/978-3-030-17949-6_9

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