相关论文: linearized inverse problem for biharmonic operator…

We establish Lipschitz stability for both the potential and the initial conditions from a single boundary measurement in the context of a hyperbolic boundary initial value problem. In our setting, the initial conditions are allowed to…

In this paper, we for the first time prove local solvability and stability of an inverse spectral problem for higher-order ($n > 3$) differential operators with distribution coefficients. The inverse problem consists in the recovery of…

This paper is concerned with the stability of the inverse boundary value problem for the perturbed fourth-order Schr\"{o}dinger equation in a bounded domain with Cauchy data. We establish stability results for the perturbed potential…

In this paper, we develop a new approach to investigation of the uniform stability for inverse spectral problems. We consider the non-self-adjoint Sturm-Liouville problem that consists in the recovery of the potential and the parameters of…

In [2] we introduced a method combining together an observability inequality and a spectral decomposition to get a logarithmic stability estimate for the inverse problem of determining both the potential and the damping coefficient in a…

This paper concerns the stability on the inverse source scattering problem for the one-dimensional Helmholtz equation in a two-layered medium. We show that the increasing stability can be achieved by using multi-frequency wave field at the…

A mathematical model describing the initial stage of the capture of oscillatory systems into autoresonance under the action of slowly varying pumping is considered. Solutions with an infinitely growing amplitude are associated with the…

We consider the partial data inverse boundary problem for the Schr\"odinger operator at a frequency $k>0$ on a bounded domain in $\mathbb{R}^n$, $n\ge 3$, with impedance boundary conditions. Assuming that the potential is known in a…

In this paper, we study the partial data inverse boundary value problem for the Schrodinger operator at a high frequency k>=1 in a bounded domain with smooth boundary in Rn, n>=3. Assuming that the potential is known in a neighborhood of…

This paper is about Holder and Lipschitz stability estimates and uniqueness theorems for some coefficient inverse problems and associated inverse source problems for a general linear parabolic equation of the second order with variable…

We consider the multi-frequency inverse source problem in the presence of a non-homogeneous medium using passive measurements. Precisely, we derive stability estimates for determining the source from the knowledge of only the imaginary part…

We consider inverse boundary value problems for polyharmonic operators and in particular, the problem of recovering the coefficients of terms up to order one. The main interest of our result is that it further relaxes the regularity…

In this article, for the radiative transport equation, we study inverse problems of determining a time independent scattering coefficient or total attenuation by boundary data on the complementary sub-boundary after making one time input of…

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…

We establish a link between stability estimates for a hyperbolic inverse problem via the Boundary Control method and the blowup of a constant appearing in the contexts of optimal unique continuation and cost of approximate controllability.

Inverse nodal problem on Dirac operator is finding the parameters in the boundary conditions, the number m and the potential function V in the Dirac equations by using a set of nodal points of a component of two component vector…

This paper investigates inverse potential problems of wave equations with cubic nonlinearity. We develop a methodology for establishing stability estimates for inversion of lower order coefficients. The new ingredients of our approach…

Solutions of bilevel optimization problems tend to suffer from instability under changes to problem data. In the optimistic setting, we construct a lifted formulation that exhibits desirable stability properties under mild assumptions that…

We propose an abstract approach to prove local uniqueness and conditional H\"older stability to non-linear inverse problems by linearization. The main condition is that, in addition to the injectivity of the linearization $A$, we need a…

In this note we devise and analyse well-posed variational formulations and operator theoretical methods for boundary value problems associated to the biharmonic operator. Of particular interest are Neumann type and over- and underdetermined…