Construction of entropy solutions for one dimensional elastodynamics via time discretisation

Sophia Demoulini; David M.A. Stuart; Athanasios E. Tzavaras

doi:10.1016/S0294-1449(00)00051-2

Construction of entropy solutions for one dimensional elastodynamics via time discretisation

Sophia Demoulini^*, David M.A. Stuart, Athanasios E. Tzavaras

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

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)
Pages (from-to)	711-731
Number of pages	21
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	17
Issue number	6
DOIs	https://doi.org/10.1016/S0294-1449(00)00051-2
State	Published - Nov 2000
Externally published	Yes

Bibliographical note

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.

ASJC Scopus subject areas

Analysis
Mathematical Physics
Applied Mathematics

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title = "Construction of entropy solutions for one dimensional elastodynamics via time discretisation",

abstract = "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).",

author = "Sophia Demoulini and Stuart, {David M.A.} and Tzavaras, {Athanasios E.}",

note = "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.",

year = "2000",

month = nov,

doi = "10.1016/S0294-1449(00)00051-2",

language = "English (US)",

volume = "17",

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journal = "Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire",

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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).

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U2 - 10.1016/S0294-1449(00)00051-2

DO - 10.1016/S0294-1449(00)00051-2

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SN - 0294-1449

VL - 17

SP - 711

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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 -

Construction of entropy solutions for one dimensional elastodynamics via time discretisation

Abstract

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