WIAS Preprint No. 1216, (2007)

Mathematical results on existence for viscoelastodynamic problems with unilateral constraints


Authors

  • Petrov, Adrien
  • Schatzman, M.

2010 Mathematics Subject Classification

  • 35L85 49J40 73D99 73V25

Keywords

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

DOI

10.20347/WIAS.PREPRINT.1216

Abstract

We study a damped wave equation and the evolution of a Kelvin-Voigt material, both problems have unilateral boundary conditions. Under appropriate regularity assumptions on the initial data, both problems possess a weak solution which is obtained as the limit of a sequence of penalized problems; the functional properties of all the traces are precisely identified through Fourier analysis, and this enables us to infer the existence of a strong solution.

Appeared in

  • SIAM J. Math. Anal., 40 (2009) pp. 1882--1904.

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