Contact problems with given time-dependent friction force in linear viscoelasticity. (English) Zbl 0718.35054

Jarušek, Jiří

Commentat. Math. Univ. Carol. 31, No. 2, 257-262 (1990).

For viscoelastic media of rate type, contact problems with time-dependent friction forces are considered under small strain assumptions. A variational formulation is given, regularized solutions are found by means of a Galerkin scheme, and the energy inequality is used to pass to the limit. The result thus proved asserts the existence and uniqueness of a weak solution. In addition, this solution depends Hölder-continuously on the friction force, and it can be shown to be bounded independently of the size of the friction force.

Reviewer: H.Engler (Bonn)

MSC:

35K85	Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators
74Hxx	Dynamical problems in solid mechanics
35L85	Unilateral problems for linear hyperbolic equations and variational inequalities with linear hyperbolic operators
35B30	Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs

Keywords:

friction forces; existence; uniqueness