TY - JOUR
T1 - Construction of entropy solutions for one dimensional elastodynamics via time discretisation
AU - Demoulini, Sophia
AU - Stuart, David M.A.
AU - Tzavaras, Athanasios E.
N1 - Funding 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.
PY - 2000/11
Y1 - 2000/11
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=0039508630&partnerID=8YFLogxK
U2 - 10.1016/S0294-1449(00)00051-2
DO - 10.1016/S0294-1449(00)00051-2
M3 - Article
AN - SCOPUS:0039508630
SN - 0294-1449
VL - 17
SP - 711
EP - 731
JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
IS - 6
ER -