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Weak solution to hyperbolic Stefan problems with memory

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Nonlinear Differential Equations and Applications NoDEA Aims and scope Submit manuscript

Abstract.

A model for Stefan problems in materials with memory is considered. This model is mainly characterized by a nonlinear Volterra integrodifferential equation of hyperbolic type. Colli and Grasselli proved the uniqueness of a weak solution under the natural assumptions on data and the existence of a strong solution for smoother data. Taking advantage of these two results and assuming just the hypotheses ensuring uniqueness, the existence of a weak solution is here shown.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy, , , , , , IT

    P. Colli

  2. Dipartimento di Matematica, Università di Pavia, Via Abbiategrasso 215, 27100 Pavia, Italy, , , , , , IT

    G. Gilardi

  3. Dipartimento di Matematica, Politecnico di Milano, Via E. Bonardi 9, 20133 Milano, Italy, , , , , , IT

    M. Grasselli

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  1. P. Colli
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  2. G. Gilardi
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  3. M. Grasselli
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Received October 19, 1995

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Colli, P., Gilardi, G. & Grasselli, M. Weak solution to hyperbolic Stefan problems with memory. NoDEA, Nonlinear differ.equ.appl. 4, 123–132 (1997). https://doi.org/10.1007/PL00001408

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  • DOI: https://doi.org/10.1007/PL00001408

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