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An Inverse Problem for a Phase-field Model in Sobolev Spaces

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Nonlinear Elliptic and Parabolic Problems

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 64))

Abstract

We prove an existence and uniqueness result for an inverse problem arising from a phase-field model with two memory kernels. More precisely, we identify the convolution memory kernels and the diffusion coefficient besides the temperature and the phase-field parameter. We prove our results in the framework of Sobolev spaces. Our fundamental tools are an optimal regularity result in the Lp spaces and fixed point arguments.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, I-20133, Milano, Italy

    F. Colombo

  2. Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, I-40126, Bologna, Italy

    D. Guidetti

Authors
  1. F. Colombo
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  2. D. Guidetti
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Editor information

Editors and Affiliations

  1. Universitá Pierre et Marie Curie, Paris

    Haim Brezis

  2. Rutgers University, New Brunswick, N.J.

    Haim Brezis

  3. Angewandte Mathematik, Universität Zurich, Winterthurerstr. 190, 8057, Zürich, Switzerland

    Michel Chipot

  4. Institute of Applied Mathematics, University of Hannover, Welfengarten 1, 30167, Hannover, Germany

    Joachim Escher

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© 2005 Birkhäuser Verlag Basel/Switzerland

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Colombo, F., Guidetti, D. (2005). An Inverse Problem for a Phase-field Model in Sobolev Spaces. In: Brezis, H., Chipot, M., Escher, J. (eds) Nonlinear Elliptic and Parabolic Problems. Progress in Nonlinear Differential Equations and Their Applications, vol 64. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7385-7_10

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