Related papers: Global Lipschitz stability for an inverse coeffici…
The globally convergent convexification numerical method is constructed for a Coefficient Inverse Problem for the Mean Field Games System. A coefficient characterizing the global interaction term is recovered from the single measurement…
We consider solutions satisfying the Neumann zero boundary condition and a linearized mean field game system in $\Omega \times (0,T)$, where $\Omega$ is a bounded domain in $\mathbb{R}^d$ and $(0,T)$ is the time interval. We prove two kinds…
In this manuscript, we establish the global well-posedness for master equations of mean field games of controls, where the interaction is through the joint law of the state and control. Our results are proved under two different conditions:…
We study in this paper stability estimates for the fault inverse problem. In this problem, faults are assumed to be planar open surfaces in a half space elastic medium with known Lam\'e coefficients. A traction free condition is imposed on…
We consider a transmission wave equation in two embedded domains in $R^2$, where the speed is $a1 > 0$ in the inner domain and $a2 > 0$ in the outer domain. We prove a global Carleman inequality for this problem under the hypothesis that…
In this paper, we investigate a discrete inverse problem of determining three unknowns, i.e. initial displacement, initial velocity and random source term, in a fully discrete approximation of one-dimensional stochastic hyperbolic equation.…
We investigate time-dependent mean-field games with superquadratic Hamiltonians and a power dependence on the measure. Such problems pose substantial mathematical challenges as the key techniques used in the subquadratic case do not extend…
This paper concerns an inverse problem for the initial boundary value problem of the two-dimensional Navier-Stokes system defined in a bounded simply connected domain with slip, vorticity boundary conditions, and a global vorticity…
We establish a Lipschitz stability estimate for the inverse problem consisting in the determination of the coefficient $\sigma(t)$, appearing in a Dirichlet initial-boundary value problem for the parabolic equation $\partial_tu-\Delta_x…
This paper introduces a notion of weak solution for the coupled system of master equations in mean field games with a major player. It extends the previously introduced notion of Lipschitz solutions in mean field games. By relying on a…
This paper focuses on stability estimates of the inverse random source problems for the polyharmonic, electromagnetic, and elastic wave equations. The source is represented as a microlocally isotropic Gaussian random field, which is defined…
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…
We consider the inverse problem for the general transport equation with external field, source term and absorption coefficient. We show that the source and the absorption coefficients can be uniquely reconstructed from the boundary…
We study stability aspects for the determination of space and time-dependent lower order perturbations of the wave operator in three space dimensions with point sources. The problems under consideration here are formally determined and we…
This paper is concerned with the stability of the inverse source problem for the damped biharmonic plate equation in three dimensions. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the…
We present stability estimates for the inverse source problem of the stochastic Helmholtz equation in two and three dimensions by either near-field or far-field data. The random source is assumed to be a microlocally isotropic generalized…
In this paper, we establish a global Carleman estimate for an Ultrahyperbolic Schr\"odinger equation. Moreover, we prove H\"older stability for the inverse problem of determining a coefficient or a source term in the Ultrahyperbolic…
This paper presents an inverse problem for the nonlinear 1-d Kuramoto-Sivashinsky (K-S) equation. More precisely, we study the nonlinear inverse problem of retrieving the anti-diffusion coefficient from the measurements of the solution on a…
We establish stability inequalities of an inverse obstacle problem for the magnetic Schr\"odinger equation. We mainly study the problem of reconstructing an unknown function defined on the obstacle boundary from two measurements performed…
We prove a global logarithmic stability estimate for the Gel'fand-Calderon inverse problem on a two-dimensional domain.