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Existence of Global Weak Solutions to a Generalized Hyperelastic-Rod Wave Equation with Source

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New Prospects in Direct, Inverse and Control Problems for Evolution Equations

Part of the book series: Springer INdAM Series ((SINDAMS,volume 10))

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Abstract

We consider a weakly dissipative hyperelastic-rod wave equation describing nonlinear dispersive dissipative waves in compressible hyperelastic rods. We endow it with a nonlinear source and establish the existence of global weak solutions for any initial condition in \(H^{1}(\mathbb{R})\).

In memory of Alfredo with a vivid remembering of his enthusiasm and dedication in fostering various activities of the inverse and control theoretic community

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Authors and Affiliations

  1. Department of Pure and Applied Mathematics, University of Padova, Via Trieste 63, 35121, Padova, Italy

    Fabio Ancona

  2. Department of Mathematics, University of Bari, Via E. Orabona 4, 70125, Bari, Italy

    Giuseppe Maria Coclite

Authors
  1. Fabio Ancona
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  2. Giuseppe Maria Coclite
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Corresponding author

Correspondence to Giuseppe Maria Coclite .

Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Università di Bologna, Bologna, Milano, Italy

    Angelo Favini

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

    Genni Fragnelli

  3. Dipartimento di Matematica, Università di Bari, Bari, Bari, Italy

    Rosa Maria Mininni

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Ancona, F., Coclite, G.M. (2014). Existence of Global Weak Solutions to a Generalized Hyperelastic-Rod Wave Equation with Source. In: Favini, A., Fragnelli, G., Mininni, R. (eds) New Prospects in Direct, Inverse and Control Problems for Evolution Equations. Springer INdAM Series, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-11406-4_2

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