Continuous data dependence for the equations of classical elastodynamics
- 1 September 1969
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 66 (2), 481-491
- https://doi.org/10.1017/s0305004100045217
Abstract
Consider a linear elastic solid occupying a bounded regular three-dimensional region B with smooth surface ∂B. The components of displacement ui referred to cartesian axes xi are then well known to satisfy the system of governing equationsin which t denotes the time variable, x = (x1, x2, x3) denotes the position vector, ρ(x) is the non-homogeneous density, assumed positive,. i(x, t) are the Cartesian components of body force per unit mass, and cijkl(x) are the non-homogeneous elasticities, which apart from certain smoothness conditions stated later, are assumed to possess the symmetryThroughout this paper, all suffixes range over the values 1, 2, 3 and the usual converition of summing over repeated indices is adopted. Except where it is in the interest of clarity we avoid explicit mention of the dependence of functions on their arguments.Keywords
This publication has 12 references indexed in Scilit:
- Stability in linear elasticityInternational Journal of Solids and Structures, 1968
- Stability of the traction boundary value problem in linear elastodynamicsInternational Journal of Engineering Science, 1968
- On the displacement boundary-value problem of linear elastodynamicsQuarterly of Applied Mathematics, 1968
- Uniqueness in classical elastodynamicsArchive for Rational Mechanics and Analysis, 1968
- On the stability of linear continuous systemsZeitschrift für angewandte Mathematik und Physik, 1965
- A uniqueness theorem for the displacement boundary-value problem of linear elastodynamicsQuarterly of Applied Mathematics, 1965
- Estimation of critical loads in elastic stability theoryArchive for Rational Mechanics and Analysis, 1964
- Effect of error in measurement of elastic constants on the solutions of problems in classical elasticityJournal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics, 1963
- A priori bounds in the First boundary value problem in elasticityJournal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics, 1961
- A note on uniqueness in classical elastodynamicsQuarterly of Applied Mathematics, 1961