Existence and uniqueness for a quasistatic frictional bilateral contact problem in thermoviscoelasticity

Rochdi, M.; Shillor, M.

doi:10.1090/qam/1770654

Authors: M. Rochdi and M. Shillor
Journal: Quart. Appl. Math. 58 (2000), 543-560
MSC: Primary 74M15; Secondary 35Q72, 74D10, 74F05, 74G25, 74G30, 74M10
DOI: https://doi.org/10.1090/qam/1770654
MathSciNet review: MR1770654
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Abstract: We prove the existence and uniqueness of the weak solution for a quasistatic thermoviscoelastic problem which describes bilateral frictional contact between a deformable body and a moving rigid foundation. The model consists of the heat equation for the temperature, the elliptic viscoelasticity system for the displacements, the SJK-Coulomb law of friction and frictional heat generation condition. The proof is accomplished in two steps. First, the existence of solutions for a regularized problem is established and a priori estimates obtained. Then the limit function, which is the weak solution of the original problem, is shown to be the unique fixed point of the solution operator when the friction coefficient is small.

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