A contact problem for bingham fluid with friction

Abstract

We consider a mathematical model which describes the stationary flow of a Bingham fluid in a domain which is partially bounded by a deformable obstacle, such as a die. The contact between the fluid and the die is modeled by a nonlocal viscoplastic friction law. We present the classical formulation of the problem and derive a variational formulation for the velocity field. We establish the existence of a weak solution and, under additional assumption, its uniqueness. The proofs are based on classical results for elliptic variational inequalities and fixed point arguments. We also establish the continuous dependence of the solution on the yield limit.

Keywords:

• Bingham fluid
• frictional contact
• normal damped response
• existence and uniqueness
• continuous dependence on yield

AMS:

• 73T05
• 35D05
• 35J55
• 35J65
• 73E60

Additional information

Notes on contributors

B. Awbi

†

M. Shillor

‡

M. Sofonea

†