Singular Perturbations in a Non-linear Viscoelasticity

Abstract

A non-linear equation in viscoelasticity of the form ρuρtt(t, x) = φ(u ρ x(t, x))x + ∫ t −∞ F (t− s)φ(ux(s, x))xds+ ρg(t, x) + f(x), t ≥ 0, x ∈ [0, 1], (0.1) u(t, 0) = u(t, 1) = 0, t ≥ 0, (0.2) u(s, x) = v(s, x), s ≤ 0, x ∈ [0, 1], (0.3) (where φ is non-linear) is studied when the density ρ of the material goes to zero. It will be shown that when ρ ↓ 0… (More)

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Cite this paper

@inproceedings{Liu2004SingularPI, title={Singular Perturbations in a Non-linear Viscoelasticity}, author={James H. Liu}, year={2004} }