11 citations · 16 across the 6 of their papers we have counts for
18 papers · 1 filter
A mollifier approach to regularize a Cauchy problem for the inhomogeneous Helmholtz equation
Pierre Marechal, Walter Simo Tao Lee, Faouzi Triki
The Cauchy problem for the inhomogeneous Helmholtz equation with non-uniform refraction index is considered. The ill-posedness of this problem is tackled by means of the variationa…
Quantitative uniqueness of continuation result related to Hopf's lemma
Mourad Choulli, Faouzi Triki, Qi Xue
The classical Hopf's lemma can be reformulated as uniqueness of continuation result. We aim in the present work to quantify this property. We show precisely that if a solution …
Recovering point sources for the inhomogeneous Helmholtz equation
Gang Bao, Yuantong Liu, Faouzi Triki
The paper is concerned with an inverse point source problem for the Helmholtz equation. It consists of recovering the locations and amplitudes of a finite number of radiative point…
Hölder stability of quantitative photoacoustic tomography based on partial data
Faouzi Triki, Qi Xue
We consider the reconstruction of the diffusion and absorption coefficients of the diffusion equation from the internal information of the solution obtained from the first step of…
Recovering the initial condition in the One-Phase Stefan problem
Chifaa Ghanmi, Saloua Mani Aouadi, Faouzi Triki
We consider the problem of recovering the initial condition in the one-dimensional one-phase Stefan problem for the heat equation from the knowledge of the position of the melting…
Coefficient identification in parabolic equations with final data
Faouzi Triki
In this work we determine the second-order coefficient in a parabolic equation from the knowledge of a single final data. Under assumptions on the concentration of eigenvalues of t…