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Abstract Volterra integrodifferential equations with applications to parabolic models with memory

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Abstract

In this paper we are concerned with local existence, regularity and continuous dependence upon the initial data of \(\epsilon \)-regular mild solutions for the abstract integrodifferential equation (1, 2). We also present a result on unique continuation and a blow-up alternative for an \(\epsilon \)-regular mild solution of (1, 2). Finally, we apply our results to three interesting models: Navier–Stokes equations with memory, diffusion equations with memory and a strongly damped plate equation with memory.

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Acknowledgments

We would like to thank the anonymous referees for their valuable suggestions. Bruno de Andrade is partially supported by CNPQ-Brazil Grant 460800/2014-0.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Sergipe, Avenue Vereador Olímpio Grande, Itabaiana, SE, Brazil

    Arlúcio Viana

  2. Departamento de Matemática, Universidade Federal de Sergipe, Avenue Rosa Else, São Cristóvão, SE, Brazil

    Bruno de Andrade

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  1. Bruno de Andrade
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de Andrade, B., Viana, A. Abstract Volterra integrodifferential equations with applications to parabolic models with memory. Math. Ann. 369, 1131–1175 (2017). https://doi.org/10.1007/s00208-016-1469-z

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