Related papers: Stability estimates for a Robin coefficient in the…
In this paper, we establish a global Carleman estimate for stochastic parabolic equations. Based on this estimate, we solve two inverse problems for stochastic parabolic equations. One is concerned with a determination problem of the…
Recent work demonstrated that alternative models to the "no-slip" boundary condition for incipient flow perturbations can produce linear instabilities that do not arise in the classical formulation. The present study introduces a Robin-type…
We improve the preceding results obtained by the first and the second authors in [3]. They concern the stability issue of the inverse problem that consists in determining the potential and the damping coefficient in a wave equation from an…
We establish in dimension $3$ a stability inequality for the problem of determining the potential in the Schr\"odinger equation from boundary measurements in the case where the potential belongs to $L^s$ with $s\in (2,3)$.
This paper is addressed to establishing an internal observability estimate for some linear stochastic hyperbolic equations. The key is to establish a new global Carleman estimate for forward stochastic hyperbolic equations in the…
We consider the Robin problem for a uniformly elliptic divergence operator with measure data on the right-hand side of the equation and an absorption term on the boundary involving blowing up terms. We prove the existence of a positive…
We consider the problem of simultaneously inferring the heterogeneous coefficient field for a Robin boundary condition on an inaccessible part of the boundary along with the shape of the boundary for the Poisson problem. Such a problem…
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,…
In a bounded domain $\Omega \subset \mathbb{R}^d$ over time interval $(0,T)$, we consider mean field game equations whose principal coefficients depend on the time and state variables with a general Hamiltonian. We attach the non-zero Robin…
In this paper, by constructing the weight functions, a global Carleman estimate for the Schrodinger equation on a tree is established, with a strong assumption on the solution. And the estimate is able to be applied to derive the Lipschitz…
In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed…
We deal with a boundary detection problem arising in nondestructive testing of materials. The problem consists in recovering an unknown portion of the boundary, where a Robin condition is satisfied, with the use of a Cauchy data pair…
This paper is focused on the study of an inverse problem for a non-self-adjoint hyperbolic equation. More precisely, we attempt to stably recover a first order coefficient appearing in a wave equation from the knowledge of Neumann boundary…
In this paper, we study local regularity of the solutions to the Stokes equations near a curved boundary under no-slip or Navier boundary conditions. We extend previous boundary estimates near a flat boundary to that near a curved boundary,…
This paper recalls a partial differential equations system, which is the linearization of a recognized fluid-elasticity interaction three-dimensional model. A collection of regularity results for the traces of the fluid variable on the…
Reformulating the incompressible Stokes equations with the velocity sought in H(curl) has recently emerged as a promising approach for the design of helicity-preserving schemes in magnetohydrodynamics and pressure-robust finite element…
A non-conventional shape optimization approach is introduced to address the identification of an obstacle immersed in a fluid described by the Stokes equation within a larger bounded domain, relying on boundary measurements on the…
We consider a half-order time-fractional diffusion equation in an arbitrary dimension and investigate inverse problems of determining the source term or the diffusion coefficient from spatial data at an arbitrarily fixed time under some…
We consider the inverse problem for time-dependent semilinear transport equations. We show that time-independent coefficients of both the linear (absorption or scattering coefficients) and nonlinear terms can be uniquely determined, in a…
This work addresses an inverse problem for a semi-discrete parabolic equation, consisting of identifying the right-hand side of the equation from solution measurements at an intermediate time and within a spatial subdomain. We apply this…