Related papers: Local Lipschitz Stability for Inverse Robin Proble…
In this paper, we consider the Stokes equations and we are concerned with the inverse problem of identifying a Robin coefficient on some non accessible part of the boundary from available data on the other part of the boundary. We first…
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…
We construct a local Lipschitz graph around a soliton of the cubic focusing NLS in three dimensions on which global solutions exist, and asymptotic stability as well as scattering holds.
We study the stability of an inverse problem for the fractional conductivity equation on bounded smooth domains. We obtain a logarithmic stability estimate for the inverse problem under suitable a priori bounds on the globally defined…
Regularization methods have been recently developed to construct stable approximate solutions to classical partial differential equations considered as final value problems. In this paper, we investigate the backward parabolic problem with…
This paper is concerned with first- and second-order optimality conditions as well as the stability for non-smooth semilinear optimal control problems involving the $L^1$-norm of the control in the cost functional. In addition to the…
We investigate the increasing stability of the inverse Schr\"{o}dinger potential problem with integer power type nonlinearities at a large wavenumber. By considering the first order linearized system with respect to the unknown potential…
In this paper, we consider the linear stability of the elliptic relative equilibria of the restricted 4-body problems where the three primaries form a Lagrangian triangle. By reduction, the linearized Poincar\'e map is decomposed to the…
Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its…
We consider the inverse hyperbolic problem of recovering all spatial dependent coefficients, which are the wave speed, the damping coefficient, potential coefficient and gradient coefficient, in a second-order hyperbolic equation defined on…
Stability is a key property of both forward models and inverse problems, and depends on the norms considered in the relevant function spaces. For instance, stability estimates for hyperbolic partial differential equations are often based on…
In the theory of second-order, nonlinear elliptic and parabolic equations, obtaining local or global gradient bounds is often a key step for proving the existence of solutions but it may be even more useful in many applications, for example…
In this paper we investigate the Bayesian approach to inverse Robin problems. These are problems for certain elliptic boundary value problems of determining a Robin coefficient on a hidden part of the boundary from Cauchy data on the…
We consider the hydrodynamic stability of homogeneous, incompressible and rotating ellipsoidal fluid masses. The latter are the simplest models of fluid celestial bodies with internal rotation and subjected to tidal forces. The classical…
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…
For linearized Navier-Stokes equations, we consider an inverse source problem of determining a spatially varying divergence-free factor. We prove the global Lipschitz stability by interior data over a time interval and velocity field at…
In this paper we present an improvement of [Math. Ann. 345 (2009), 213--243], where the authors proved a result concerning continuous dependence for backward parabolic operators whose coefficients are Log-Lipschitz in $t$ and $C^2$ in $x$.…
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…
We establish sharp global regularity results for solutions to nonhomogeneous, nonunifomrly elliptic systems with zero boundary conditions. In particular, we obtain everywhere Lipschitz continuity under borderline Lorentz assumptions on the…
Partial inverse problems are studied for Sturm-Liouville operators with a discontinuity. The main results of the paper are local solvability and stability of the considered inverse problems. Our approach is based on a constructive algorithm…