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Existence theory to the equations in viscoelasticity at finite deformations
Author(s) -
Jäpel Irg
Publication year - 1998
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19980781548
Subject(s) - viscoelasticity , dimension (graph theory) , nonlinear system , mathematical analysis , mathematics , boundary value problem , string (physics) , constitutive equation , space (punctuation) , boundary (topology) , motion (physics) , equations of motion , classical mechanics , physics , mathematical physics , pure mathematics , computer science , finite element method , quantum mechanics , thermodynamics , operating system
The usual equations of motion combined with a constitutive law for a viscoelastic metal string lead us to a nonlinear, strictly hyperbolic system in one space dimension. The system under consideration is associated with a free damping boundary condition and continuously differentiable initial conditions. In the case of small initial data it is possible to prove global existence of a classical solution, whereas for large data a blow up result is obtained.