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    Measure-valued solutions for the equations of polyconvex adiabatic thermoelasticity

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    thermo-poly-mv_SUBMIT_arxiv.pdf
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    Description:
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    Type
    Article
    Authors
    Christoforou, Cleopatra
    Galanopoulou, Myrto Maria
    Tzavaras, Athanasios cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2019-08-30
    Online Publication Date
    2019-08-30
    Print Publication Date
    2019
    Embargo End Date
    2020-01-01
    Permanent link to this record
    http://hdl.handle.net/10754/656727
    
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    Abstract
    For the system of polyconvex adiabatic thermoelasticity, we define a notion of dissipative measure-valued solution, which can be considered as the limit of a viscosity approximation. We embed the system into a symmetrizable hyperbolic one in order to derive the relative entropy. Exploiting the weak-stability properties of the transport and stretching identities, we base our analysis in the original variables, instead of the symmetric ones (in which the entropy is convex) and we prove measure-valued weak versus strong uniqueness using the averaged relative entropy inequality.
    Citation
    Christoforou, C., Galanopoulou, M., & E. Tzavaras, A. (2019). Measure-valued solutions for the equations of polyconvex adiabatic thermoelasticity. Discrete & Continuous Dynamical Systems - A, 39(11), 6175–6206. doi:10.3934/dcds.2019269
    Publisher
    American Institute of Mathematical Sciences (AIMS)
    Journal
    Discrete & Continuous Dynamical Systems - A
    DOI
    10.3934/dcds.2019269
    Additional Links
    http://aimsciences.org//article/doi/10.3934/dcds.2019269
    ae974a485f413a2113503eed53cd6c53
    10.3934/dcds.2019269
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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