The existence of solutions in nonlinear elastodynamics (Q1369477)
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scientific article; zbMATH DE number 1076538
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The existence of solutions in nonlinear elastodynamics |
scientific article; zbMATH DE number 1076538 |
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The existence of solutions in nonlinear elastodynamics (English)
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27 September 1998
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The author discusses a nonlinear initial-boundary value problem of elastodynamics, in which the equation of motion and the strain-displacement relation are linear, and the stress is a nonlinear function of the strains generated by a potential \(W\). It is shown that if: (i) \(W\) is a smooth function of the strains, (ii) \(W\) satisfies a convex-type inequality, and (iii) the data are suitably restricted, then the initial-boundary value problem has a unique solution in a functional space of the Sobolev type.
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unique solution in functional space of Sobolev type
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initial-boundary value problem
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strain-displacement relation
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potential
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convex-type inequality
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