Solvability of a pseudodifferential linear complementarity problem related to a viscoelastodynamic contact model

Abstract

This paper focus on a simplified viscoelastic problem subjected to unilateral boundary conditions. The problem is reduced to a pseudodifferential linear complementarity problem using Fourier techniques. Under appropriate regularity assumptions on the data, the diagonal process is employed to prove the existence result to this pseudodifferential linear complementarity problem.

Keywords:

• Viscoelasticity
• Signorini conditions
• penalty method
• traces
• convolution
• variational inequality

AMS Subject Classifications:

• 35L85
• 49J40
• 73D99
• 73V25

Acknowledgements

I am grateful to M. Schatzman for all the simulating discussions as well as to have improved most of the results presented here thanks to her always relevant remarks. The final form of the present work owes very much to her disinterested advices. For all these reasons, she is morally the co-author of this paper. The author warmly thanks also A. Heibig for fruitful discussions.

Notes

No potential conflict of interest was reported by the author.