68 research outputs found
Interior feedback stabilization of wave equations with dynamic boundary delay
In this paper we consider an interior stabilization problem for the wave
equation with dynamic boundary delay.We prove some stability results under the
choice of damping operator. The proof of the main result is based on a
frequency domain method and combines a contradiction argument with the
multiplier technique to carry out a special analysis for the resolvent
Determining a boundary coefficient in a dissipative wave equation: Uniqueness and directional lipschitz stability
We are concerned with the problem of determining the damping boundary
coefficient appearing in a dissipative wave equation from a single boundary
measurement. We prove that the uniqueness holds at the origin provided that the
initial condition is appropriately chosen. We show that the choice of the
initial condition leading to uniqueness is related to a fine version of unique
continuation property for elliptic operators. We also establish a Lipschitz
directional stability estimate at the origin, which is obtained by a
linearization process
Logarithmic stability in determining two coefficients in a dissipative wave equation. Extensions to clamped Euler-Bernoulli beam and heat equations
We are concerned with the inverse problem of determining both the potential
and the damping coefficient in a dissipative wave equation from boundary
measurements. We establish stability estimates of logarithmic type when the
measurements are given by the operator who maps the initial condition to
Neumann boundary trace of the solution of the corresponding initial-boundary
value problem. We build a method combining an observability inequality together
with a spectral decomposition. We also apply this method to a clamped
Euler-Bernoulli beam equation. Finally, we indicate how the present approach
can be adapted to a heat equation
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