Geodesic
Existence of Global Weak Solutions to the Equations of One-Dimensional Nonlinear Thermoviscoelasticity with Discontinuous Data
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 11-19

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The existence of global weak solutions to initial–boundary value problems for a system of quasilinear differential equations describing the dynamics of a one-dimensional Voigt-type thermoviscoelastic body is established. The initial and boundary data may be discontinuous functions. Only physically natural requirements are imposed on the data. In particular, it is required that the initial velocity and initial temperature should be such that the full energy is finite. The density of heat sources and a boundary heat flux may be functions from $L_1$. The functions defining the properties of the body may also be discontinuous in $x$. 
@article{TM_2002_236_a1,
     author = {A. A. Amosov},
     title = {Existence of {Global} {Weak} {Solutions} to the {Equations} of {One-Dimensional} {Nonlinear} {Thermoviscoelasticity} with {Discontinuous} {Data}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {11--19},
     publisher = {mathdoc},
     volume = {236},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2002_236_a1/}
}
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A. A. Amosov. Existence of Global Weak Solutions to the Equations of One-Dimensional Nonlinear Thermoviscoelasticity with Discontinuous Data. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 11-19. http://geodesic.mathdoc.fr/item/TM_2002_236_a1/