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An initial boundary value problem for modeling a piezoelectric dipolar body

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Abstract

This study deals with the first initial boundary value problem in elasticity of piezoelectric dipolar bodies. We consider the most general case of an anisotropic and inhomogeneous elastic body having a dipolar structure. For two different types of restrictions imposed on the problem data, we prove two results regarding the uniqueness of solution, by using a different but accessible method. Then, the mixed problem is transformed in a temporally evolutionary equation on a Hilbert space, conveniently constructed based on the problem data. With the help of a known result from the theory of semigroups of operators, the existence and uniqueness of the weak solution for this equation are proved.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Transilvania University of Brasov, 500093, Brasov, Romania

    Marin Marin

  2. Faculty of Mechanical Engineering, Esslingen University of Applied Sciences, 73728, Esslingen, Germany

    Andreas Öchsner

Authors
  1. Marin Marin
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  2. Andreas Öchsner
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Correspondence to Marin Marin.

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Marin, M., Öchsner, A. An initial boundary value problem for modeling a piezoelectric dipolar body. Continuum Mech. Thermodyn. 30, 267–278 (2018). https://doi.org/10.1007/s00161-017-0599-1

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  • DOI: https://doi.org/10.1007/s00161-017-0599-1

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