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Global existence for a nonlinear system in thermoviscoelasticity with nonconvex energy


Reference:

Zimmer, J., 2004. Global existence for a nonlinear system in thermoviscoelasticity with nonconvex energy. Journal of Mathematical Analysis and Applications, 292 (2), pp. 589-604.

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    Official URL:

    http://dx.doi.org/10.1016/j.jmaa.2003.12.010

    Abstract

    A three-dimensional thermoviscoclastic system derived from the balance laws of momentum and energy is considered. To describe structural phase transitions in solids, the stored energy function is not assumed to be convex as a function of the deformation gradient. A novel feature for multidimensional, nonconvex, and nonisothermal problems is that no regularizing higher-order terms are introduced. The mechanical dissipation is not linearized. We prove existence global in time. The approach is based on a fixed-point argument using an implicit time discretization and the theory of renormalized solutions for parabolic equations with L-1 data. (C) 2004 Elsevier Inc. All rights reserved.

    Details

    Item Type Articles
    CreatorsZimmer, J.
    DOI10.1016/j.jmaa.2003.12.010
    DepartmentsFaculty of Science > Mathematical Sciences
    Publisher Statementthermo.pdf: Published version can be found at http://dx.doi.org/10.1016/j.jmaa.2003.12.010
    RefereedYes
    StatusPublished
    ID Code7192
    Additional InformationID number: ISI:000221110800021

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