Abstract
We study coupled systems of nonlinear initial boundary value problems from continuum mechanics, where each system is of higher order, and of hyperbolic or parabolic type. Our goal is to derive sufficient conditions on the underlying constitutive equations, such that the coupled problem admits a unique smooth solution. These conditions constitute the mathematical counterpart to those conditions obtained by exploiting the second law of thermodynamics. For the proofs of our results we refer the reader to [3], [4] and [5].
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Ebenfeld, S. (2003). Initial Boundary Value Problems in Continuum Mechanics. In: Hutter, K., Baaser, H. (eds) Deformation and Failure in Metallic Materials. Lecture Notes in Applied and Computational Mechanics, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36564-8_11
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DOI: https://doi.org/10.1007/978-3-540-36564-8_11
Publisher Name: Springer, Berlin, Heidelberg
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