Journal
APPLIED MATHEMATICAL MODELLING
Volume 80, Issue -, Pages 827-839Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2019.11.022
Keywords
Microtemperatures; Dipolar material; Micro-particles; Semigroup; Continuous dependence; Finite element method
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In this study we formulate the mixed initial boundary value problem for a dipolar thermoelastic material whose micro-particles possess microtemperatures. Then this mixed problem is transformed in a Cauchy problem attached to a temporally equation of evolution on a specific Hilbert space, which will be suitably chosen. As such, we will be able to use certain results specific to the theory of the semigroups of contractions in order to obtain the existence and uniqueness of the solution for our problem. The theory of semigroups also facilitates our approach regarding the continuous dependence of the solution upon initial data and loads. Finally, we reduce our model to the isotropic case and perform numerical simulations for the corresponding system of partial differential equations by means of the finite element method. (C) 2019 Elsevier Inc. All rights reserved.
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