It is shown that the variational approximation scheme for one-dimensional elastodynamics given by time discretisation converges, subsequentially, weakly and a.e. to a weak solution which satisfies the entropy inequalities. We also prove convergence under the restriction of positive spatial derivative (for longitudinal motions).
|Original language||English (US)|
|Number of pages||21|
|Journal||Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire|
|State||Published - Nov 2000|
Bibliographical noteFunding Information:
This research was commenced in IHES and Ecole Polytechnique, Paris and concluded in FORTH, Crete; we thank these institutions for their support. S. Demoulini was partially supported by TMR Marie Curie grant ERBFMBICT972343. D. Stuart was partially supported by NSF grants 9304580 and 9623463 and EPSRC AF/98/2492. A. Tzavaras was partially supported by NSF grant DMS-9971934, ONR grant N00014-93-1-0015 and the TMR project HCL grant ERBFMRXCT960033.
ASJC Scopus subject areas
- Mathematical Physics
- Applied Mathematics