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Well-Posedness of Volterra Integro-Differential Equations with Fractional Exponential Kernels

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Differential and Difference Equations with Applications (ICDDEA 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 333))

Abstract

Well-defined solvability of initial boundary value problems for integro-differential equations with unbounded operator coefficients in Hilbert spaces is established in weighted Sobolev spaces on the positive semi-axis. The principal part of such equations is an abstract hyperbolic equation perturbed by terms with Volterra integral operators. These equations can be regarded as an abstract generalization of the Gurtin-Pipkin integro-differential equation that describes heat transfer in materials with memory and has a number of other applications. Numerous problems of hereditary mechanics and thermal physics have motivated the study of such equations.

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Acknowledgements

This work was supported by Russian Foundation for Basic Research (grant no. 20-01-00288 A).

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Authors and Affiliations

  1. Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow, 119991, Russian Federation

    N. A. Rautian

  2. Lomonosov Moscow State University, Moscow Center for Fundamental and Applied Mathematics, Moscow, Russian Federation

    N. A. Rautian

Authors
  1. N. A. Rautian
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Correspondence to N. A. Rautian .

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Editors and Affiliations

  1. Department of Exact Sciences and Engineering, Military Academy, Lisbon, Portugal

    Sandra Pinelas

  2. Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, USA

    John R. Graef

  3. Mathematik und Didaktik, Katholische Universität Eichstätt, Eichstätt, Bayern, Germany

    Stefan Hilger

  4. Huazhong University of Science and Technology, Wuhan, Hubei, China

    Peter Kloeden

  5. Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi, Xanthi, Greece

    Christos Schinas

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Rautian, N.A. (2020). Well-Posedness of Volterra Integro-Differential Equations with Fractional Exponential Kernels. In: Pinelas, S., Graef, J.R., Hilger, S., Kloeden, P., Schinas, C. (eds) Differential and Difference Equations with Applications. ICDDEA 2019. Springer Proceedings in Mathematics & Statistics, vol 333. Springer, Cham. https://doi.org/10.1007/978-3-030-56323-3_39

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