An approximation theorem for functionals, with applications in continuum mechanics
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Publication:773420
DOI10.1007/BF00276168zbMath0097.16403MaRDI QIDQ773420
Bernard D. Coleman, Walter Noll
Publication date: 1960
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
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Cites Work
- A mathematical theory of the mechanical behavior of continuous media
- On certain steady flows of general fluids
- The theory of matrix polynomials and its application to the mechanics of isotropic continua
- Finite integrity bases for five or fewer symmetric 3 \(\times\) 3 matrices
- Further results in the theory of matrix polynomials
- RECENT RESULTS IN THE CONTINUUM THEORY OF VISCOELASTIC FLUIDS*