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A global existence result for the quasistatic frictional contact problem with normal compliance. (English) Zbl 0761.73104
Unilateral problems in structural analysis IV, Proc. 4th Meet., Capri/Italy 1989, ISNM 101, 85-111 (1991).
Summary: [For the entire collection see Zbl 0745.00040.]
We consider the quasistatic problem of the contact of an elastic body with a rigid foundation in the presence of friction. The contact condition is taken as a power law normal compliance. We prove, for forces and initial data that are not too large, the existence of a solution $${\mathbf u}$$ such that $${\mathbf u}\in C([0,T];{\mathbf H}^ 1(\Omega))$$ and $$d{\mathbf u}/dt\in L^ 2([0,T];{\mathbf H}^ 2(\Omega))$$. The main tools are from the theory of differential inclusions.

##### MSC:
 74A55 Theories of friction (tribology) 74M15 Contact in solid mechanics 74S30 Other numerical methods in solid mechanics (MSC2010) 74P10 Optimization of other properties in solid mechanics 49J40 Variational inequalities