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Displaying 81 –
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129
The stabilization of solutions to an abstract differential equation is investigated. The initial value problem is considered in the form of an integral equation. The equation is solved by means of the Banach contraction mapping theorem or the Schauder fixed point theorem in the space of functions decreasing to zero at an appropriate rate. Stable manifolds for singular perturbation problems are compared with each other. A possible application is illustrated on an initial-boundary-value problem for...
This article investigates the long-time behaviour of parabolic scalar conservation laws of the type , where and the flux is periodic in . More
specifically, we consider the case when the initial data is an disturbance of a stationary periodic solution. We show, under polynomial growth assumptions on the flux, that the difference between u
and the stationary solution behaves in norm like a self-similar profile for large times. The proof uses a time and space change of variables which is...
The studies considered here are concerend with a linear thermoelastic Bresse system with delay term in the feedback. The heat conduction is also given by Cattaneo's law. Under an appropriate assumption between the weight of the delay and the weight of the damping, we prove the well-posedness of the problem using the semigroup method. Furthermore, based on the energy method, we establish an exponential stability result depending of a condition on the constants of the system that was first considered...
We consider a linear coupled system of quasi-electrostatic equations which govern the evolution of a 3-D layered piezoelectric body. Assuming that a dissipative effect is effective at the boundary, we study the uniform stabilization problem. We prove that this is indeed the case, provided some geometric conditions on the region and the interfaces hold. We also assume a monotonicity condition on the coefficients. As an application, we deduce exact controllability of the system with boundary control...
We consider a dynamical one-dimensional nonlinear von Kármán model for beams depending on a parameter and study its asymptotic behavior for large, as . Introducing appropriate damping mechanisms we show that the energy of solutions of the corresponding damped models decay exponentially uniformly with respect to the parameter . In order for this to be true the damping mechanism has to have the appropriate scale with respect to . In the limit as we obtain damped Berger–Timoshenko beam models...
We consider a dynamical one-dimensional
nonlinear von Kármán model for beams
depending on a parameter ε > 0 and study
its asymptotic behavior for t large, as ε → 0. Introducing appropriate damping
mechanisms we show that the energy of solutions
of the corresponding damped models decay
exponentially uniformly with respect to the
parameter ε. In order for this to be true the
damping mechanism has to have the appropriate
scale with respect to ε. In the limit as ε → 0 we obtain damped Berger–Timoshenko...
We study the stabilization of global solutions of the Kawahara (K) equation in a bounded interval, under the effect of a localized damping mechanism. The Kawahara equation is a model for small amplitude long waves. Using multiplier techniques and compactness arguments we prove the exponential decay of the solutions of the (K) model. The proof requires of a unique continuation theorem and the smoothing effect of the (K) equation on the real line, which are proved in this work.
We study the stabilization of global solutions of the
Kawahara (K) equation in a bounded interval, under the effect of
a localized damping mechanism. The Kawahara equation is a model
for small amplitude long waves. Using multiplier techniques and
compactness arguments we prove the
exponential decay of the solutions of the (K) model. The proof
requires of a unique continuation theorem and the smoothing effect
of the (K) equation on the real line, which are proved in this work.
Currently displaying 81 –
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129