A higher-order porous thermoelastic problem with microtemperatures

In this paper, we study a porous thermoelastic problem with microtemperatures assuming parabolic higher order in time derivatives for the thermal variables. The model is derived and written as a coupled linear system. Then, a uniqueness result is proved by using the logarithmic convexity method in t...

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Bibliographic Details
Published inApplied mathematics and mechanics Vol. 44; no. 11; pp. 1911 - 1926
Main Authors Fernández, J. R., Quintanilla, R.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2023
Springer Nature B.V
Department of Applied Mathematics I,University of Vigo,ETSI de Telecomunicación Campus As Lagoas Marcosende s/n,Vigo 36310,Spain%Department of Mathematics,Polytechnical University of Catalunya,Terrassa 08222,Barcelona,Spain
EditionEnglish ed.
Subjects
Applications of Mathematics
Classical Mechanics
Convexity
Fluid- and Aerodynamics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Partial Differential Equations
74F05
74H25
logarithmic convexity method
higher order
37N15
74H20
O414.1
microtemperature
existence and uniqueness
thermoelasticity
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Summary:In this paper, we study a porous thermoelastic problem with microtemperatures assuming parabolic higher order in time derivatives for the thermal variables. The model is derived and written as a coupled linear system. Then, a uniqueness result is proved by using the logarithmic convexity method in the case that we do not assume that the mechanical energy is positive definite. Finally, the existence of the solution is obtained by introducing an energy function and applying the theory of linear semigroups.
ISSN:0253-4827
1573-2754
DOI:10.1007/s10483-023-3049-8