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A semigroup of contractions in elasticity of porous bodies

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Abstract

The mixed initial-boundary value problem in the context of elasticity of porous bodies having a dipolar structure is considered. By means of a semigroup of contractions, we can obtain some results regarding the existence and uniqueness of solutions for this mixed problem, after proving the equivalence between this problem and a Cauchy problem attached to an abstract equation of evolution. Also, by means of this Cauchy problem, we deduce two continuous dependence results, regarding the supply terms of the original mixed problem and upon initial data.

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  • 05 May 2021

    This article was updated due to the missing funding note.

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Correspondence to M. Marin.

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Communicated by Andreas Öchsner.

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Marin, M., Öchsner, A., Ellahi, R. et al. A semigroup of contractions in elasticity of porous bodies. Continuum Mech. Thermodyn. 33, 2027–2037 (2021). https://doi.org/10.1007/s00161-021-00992-7

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Keywords

  • Equations of evolution
  • Semigroup
  • Contractions
  • Porous bodies
  • Continuous dependence