Mathematical results on existence for viscoelastodynamic problems with unilateral constraints
- Petrov, Adrien
- Schatzman, M.
2010 Mathematics Subject Classification
- 35L85 49J40 73D99 73V25
- Viscoelasticity, Signorini conditions, penalty method, traces, variational inequality, convolution
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.
- SIAM J. Math. Anal., 40 (2009) pp. 1882--1904.