225 research outputs found
Inverse observability inequalities for integrodifferential equations in square domains
In this paper we will consider oscillations of square viscoelastic membranes by adding to the wave equation another term, which takes into account the memory. To this end, we will study a class of integrodifferential equations in square domains. By using accurate estimates of the spectral properties of the integrodifferential operator, we will prove an inverse observability inequality
A Mathematical Model for Signal's Energy at the Output of an Ideal DAC
The presented research work considers a mathematical model for energy of the
signal at the output of an ideal DAC, in presence of sampling clock jitter.
When sampling clock jitter occurs, the energy of the signal at the output of
ideal DAC does not satisfies a Parseval identity. Nevertheless, an estimation
of the signal energy is here shown by a direct method involving sinc functions
Reachability problems for a wave-wave system with a memory term
We solve the reachability problem for a coupled wave-wave system with an integro-differential term. The control functions act on one side of the boundary. The estimates on the time is given in terms of the parameters of the problem and they are explicitly computed thanks to Ingham type results. Nevertheless some restrictions appear in our main results. The Hilbert Uniqueness Method is briefly recalled. Our findings can be applied to concrete examples in viscoelasticity theor
Solutions of fractional logistic equations by Euler's numbers
In this paper, we solve in the convergence set, the fractional logistic
equation making use of Euler's numbers. To our knowledge, the answer is still
an open question. The key point is that the coefficients can be connected with
Euler's numbers, and then they can be explicitly given. The constrained of our
approach is that the formula is not valid outside the convergence set,
The idea of the proof consists to explore some analogies with logistic
function and Euler's numbers, and then to generalize them in the fractional
case.Comment: Euler's numbers, Biological Application, Fractional logistic equatio
Observability of rectangular membranes and plates on small sets
Since the works of Haraux and Jaffard we know that rectangular plates may be
observed by subregions not satisfying the geometrical control condition. We
improve these results by observing only on an arbitrarily short segment inside
the domain. The estimates may be strengthened by observing on several
well-chosen segments.
In the second part of the paper we establish various observability theorems
for rectangular membranes by applying Mehrenberger's recent generalization of
Ingham's theorem.Comment: 22 pages, 8 figure
Control problems for weakly coupled systems with memory
We investigate control problems for wave-Petrovsky coupled systems in the
presence of memory terms. By writing the solutions as Fourier series, we are
able to prove Ingham type estimates, and hence reachability results. Our
findings have applications in viscoelasticity theory and linear acoustic
theory
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