We prove logarithmic stability in the parabolic inverse problem of determining the space-varying factor in the source, by a single partial boundary measurement of the solution to the heat equation in an infinite closed waveguide, with homogeneous initial and Dirichlet data.
This paper is concerned with an inverse source problem for the stochastic biharmonic operator wave equation. The driven source is assumed to be a microlocally isotropic Gaussian random field with its covariance operator being a classical pseudo-diffe
rential operator. The well-posedness of the direct problem is examined in the distribution sense and the regularity of the solution is discussed for the given rough source. For the inverse problem, the strength of the random source, involved in the principal symbol of its covariance operator, is shown to be uniquely determined by a single realization of the magnitude of the wave field averaged over the frequency band with probability one. Numerical experiments are presented to illustrate the validity and effectiveness of the proposed method for the case that the random source is the white noise.
This paper investigates the identification of two coefficients in a coupled hyperbolic system with an observation on one component of the solution. Based on the the Carleman estimate for coupled wave equations a logarithmic type stability result is o
btained by measurement data only in a suitably chosen subdomain under the assumption that the coefficients are given in a neighborhood of some subboundary.
In this paper, we study an inverse coefficients problem for two coupled Schr{o}dinger equations with an observation of one component of the solution. The observation is done in a nonempty open subset of the domain where the equations hold. A logarith
mic type stability result is obtained. The main method is based on the Carleman estimate for coupled Schr{o}dinger equations and coupled heatn equations, and the Fourier-Bros-Iagolnitzer transform.
The main aim of this paper is to solve an inverse source problem for a general nonlinear hyperbolic equation. Combining the quasi-reversibility method and a suitable Carleman weight function, we define a map of which fixed point is the solution to th
e inverse problem. To find this fixed point, we define a recursive sequence with an arbitrary initial term by the same manner as in the classical proof of the contraction principle. Applying a Carleman estimate, we show that the sequence above converges to the desired solution with the exponential rate. Therefore, our new method can be considered as an analog of the contraction principle. We rigorously study the stability of our method with respect to noise. Numerical examples are presented.
In this paper we prove stable determination of an inverse boundary value problem associated to a magnetic Schrodinger operator assuming that the magnetic and electric potentials are essentially bounded and the magnetic potentials admit a Holder-type modulus of continuity in the sense of $L^2$.
Yavar Kian
,Diomba Sambou
,Eric Soccorsi
.
(2016)
.
"Logarithmic stability inequality in an inverse source problem for the heat equation on a waveguide"
.
\\'Eric Soccorsi
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