819 research outputs found
Stability properties for some non-autonomous dissipative phenomena proved by families of Liapunov functionals
We prove some new results regarding the boundedness, stability and
attractivity of the solutions of a class of initial-boundary-value problems
characterized by a quasi-linear third order equation which may contain
time-dependent coefficients. The class includes equations arising in
Superconductor Theory, and in the Theory of Viscoelastic Materials. In the
proof we use a family of Liapunov functionals W depending on two parameters,
which we adapt to the `error', i.e. to the size of the chosen neighbourhood of
the null solution.Comment: Latex file, 12 page
Existence, uniqueness and stability for a class of third order dissipative problems depending on time
We prove new results regarding the existence, uniqueness, (eventual)
boundedness, (total) stability and attractivity of the solutions of a class of
initial-boundary-value problems characterized by a quasi-linear third order
equation which may contain time-dependent coefficients. The class includes
equations arising in Superconductor Theory and in the Theory of Viscoelastic
Materials. In the proof we use a Liapunov functional V depending on two
parameters, which we adapt to the characteristics of the problem.Comment: Latex file, 20 pages, 7 figures. To appear in "Nonlinear Analysis:
Theory, Methods & Applications
Timoshenko systems with fading memory
The decay properties of the semigroup generated by a linear Timoshenko system
with fading memory are discussed. Uniform stability is shown to occur within a
necessary and sufficient condition on the memory kernel
Averaging of equations of viscoelasticity with singularly oscillating external forces
Given , we consider for the nonautonomous
viscoelastic equation with a singularly oscillating external force together with the
{\it averaged} equation Under suitable assumptions on
the nonlinearity and on the external force, the related solution processes
acting on the natural weak energy space
are shown to possess uniform attractors . Within the
further assumption , the family turns out to
be bounded in , uniformly with respect to .
The convergence of the attractors to the attractor
of the averaged equation as is also
established
General decay of the solution for a viscoelastic wave equation with a time-varying delay term in the internal feedback
In this paper we consider a viscoelastic wave equation with a time-varying
delay term, the coefficient of which is not necessarily positive. By
introducing suitable energy and Lyapunov functionals, under suitable
assumptions, we establish a general energy decay result from which the
exponential and polynomial types of decay are only special cases.Comment: 11 page
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