# Lack of Exponential Stability in Timoshenko Systems with Flat Memory Kernels

Lack of Exponential Stability in Timoshenko Systems with Flat Memory Kernels We analyze the decay properties of the solution semigroup generated by the linear Timoshenko system \begin{aligned} \left\{ \begin{array}{l} \rho _1 \varphi _{tt} -\kappa (\varphi _x +\psi )_x = 0\\ \displaystyle \rho _2 \psi _{tt} -b\psi _{xx} +\int _0^\infty \mu (s)\psi _{xx}(t-s)\,\mathrm{d}s+\kappa (\varphi _x +\psi )= 0 \end{array}\right. \end{aligned} ρ 1 φ t t - κ ( φ x + ψ ) x = 0 ρ 2 ψ t t - b ψ x x + ∫ 0 ∞ μ ( s ) ψ x x ( t - s ) d s + κ ( φ x + ψ ) = 0 in presence of a flat (i.e. piecewise constant) memory kernel $$\mu$$ μ . In this situation, the uniform decay of the solutions does not occur, also when the two equations exhibit the same propagation speed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# Lack of Exponential Stability in Timoshenko Systems with Flat Memory Kernels

, Volume 71 (1) – Feb 1, 2015
15 pages

/lp/springer_journal/lack-of-exponential-stability-in-timoshenko-systems-with-flat-memory-dsD7h9GslX
Publisher
Springer US
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-014-9253-5
Publisher site
See Article on Publisher Site

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