Related papers: Well-posedness of the Goursat problem and stabilit…

We are concerned with the problem of determining the nonlinear term in a semilinear elliptic equation by boundary measurements. Precisely, we improve [5, Theorem 1.3], where a logarithmic type stability estimate was proved. We show actually…

This paper is concerned with an inverse source problem for the three-dimensional Helmholtz equation by a single boundary measurement at a fixed frequency. We show the Lipschitz stability under the assumption that the source function is…

This paper is devoted to the investigation of the backward problem for a multi-term time-fractional diffusion equation. Backward problems for fractional diffusion equations are typically studied using regularization methods due to their…

This paper deals with an inverse source problem for the $1$D time-fractional diffusion equation by using boundary measurement. The conditional stability in identification of the unknown source term is proved on the basis of the Fourier…

In this paper, we will study increasing stability in the inverse source problem for the Helmholtz equation in the plane when the source term is assumed to be compactly supported in a bounded domain $\Omega$ with sufficiently smooth…

The initial-value problem for a particular bidirectional Whitham system modelling surface water waves is under consideration. This system was recently introduced in [4]. It is numerically shown to be stable and a good approximation to the…

The study of resonances (and well-posedness) for complex systems under time-periodic loading is of broad interest in application. The work of Galdi et al.~(2014) connects asymptotic stability of solutions to an unforced Cauchy problem to…

We apply methods of the so-called `inverse problem of the calculus of variations' to the stabilization of an equilibrium of a class of two-dimensional controlled mechanical systems. The class is general enough to include, among others, the…

In this paper, we prove the global well-posedness for the 3D rotating Navier-Stokes equations in the critical functional framework. Especially, this result allows to construct global solutions for a class of highly oscillating initial data.

We establish global well-posedness and scattering results for the logarithmically energy-supercritical nonlinear wave equation, under the assumption that the initial data satisfies a partial symmetry condition. These results generalize and…

We derive conditional stability estimates for inverse scattering problems related to time harmonic magnetic Schr\"odinger equation. We prove logarithmic type estimates for retrieving the magnetic (up to a gradient) and electric potentials…

In this work, we investigate the stability issue of the inverse problem of determining the locations and time-dependent amplitudes of point sources in a parabolic equation with a non-self adjoint elliptic operator from boundary…

Professor Pierre Sabatier contributed much to the study of inverse problems in theory and practice. Two of these contributions were a focus on theory that actually supports practice, and the identification of well-posed aspects of inverse…

A major problem in solving multi-waves inverse problems is the presence of critical points where the collected data completely vanishes. The set of these critical points depend on the choice of the boundary conditions, and can be directly…

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 the inverse photoacoustic tomography (PAT). In practice, the…

Using uniform global Carleman estimates for discrete elliptic and semi-discrete hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in a semi-discrete wave equation,…

We establish the well-posedness of an initial-boundary value problem for a general class of time-fractional, advection-diffusion-reaction equations, allowing space- and time-dependent coefficients as well as initial data that may have low…

We investigate the obstacle problem for generalized Dean--Kawasaki equations driven by correlated conservative noise, establishing the existence, uniqueness, and $L^1$-stability of stochastic kinetic solutions. Our core strategy combines a…

We consider the inverse problem of determining some class of nonlinear terms appearing in an elliptic equation from boundary measurements. More precisely, we study the stability issue for this class of inverse problems. Under suitable…

In this paper we prove that the Cauchy problem for first-order quasi-linear systems of partial differential equations is ill-posed in Gevrey spaces, under the assumption of an initial ellipticity. The assumption bears on the principal…