Related papers: Inverse problem for a parabolic system with two co…

We consider backward problems for semilinear coupled parabolic systems in bounded domains. We prove conditional stability estimates for linear and semilinear systems of strongly coupled parabolic equations involving general semilinearities.…

We consider initial boundary value problems with the homogeneous Neumann boundary condition. Given an initial value, we establish the uniqueness in determining a spatially varying coefficient of zeroth-order term by a single measurement of…

We propose a globally convergent computational technique for the nonlinear inverse problem of reconstructing the zero-order coefficient in a parabolic equation using partial boundary data. This technique is called the "reduced dimensional…

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.…

This paper aims to establish null controllability for systems coupled by two backward fourth order stochastic parabolic equations. The main goal is to control both equations with only one control act on the drift term. To achieve this, we…

We prove a Carleman estimate for a one-dimensional parabolic equation which degenerates at one extremity of the domain and has a bounded, time dependent coefficient multiplying the diffusion term. Then we use the estimate to show the null…

This review examines classical and recent results on controllability and inverse problems for hyperbolic and dispersive equations with dynamic boundary conditions. We aim to illustrate the applicability of Carleman estimates to establish…

This work addresses controllability properties for some systems of partial differential equations in which the main feature is the coupling through nonlocal integral terms. In the first part, we study a nonlinear parabolic-elliptic system…

We consider inverse problems for the first and half order time fractional equation. We establish the stability estimates of Lipschitz type in inverse source and inverse coefficient problems by means of the Carleman estimates.

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…

The main purpose of this work is to study an inverse coefficient problem for the telegrapher's equations on a tree-shaped network. To analyze the stability for this inverse problem, Carleman estimate is established first. Based upon this…

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…

The key tool of this paper is a new Carleman estimate for an arbitrary parabolic operator of the second order for the case of reversed time data. This estimate works on an arbitrary time interval. On the other hand, the previously known…

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…

This paper is devoted to the study of the null and approximate controllability for some classes of linear coupled parabolic systems with less controls than equations. More precisely, for a given bounded domain in R^N, we consider a system…

This paper is concerned with the null controllability for linear backward stochastic parabolic equations with dynamic boundary conditions and convection terms. Using the classical duality argument, the null controllability is obtained via…

We study an inverse problem involving the restoration of two radiative potentials, not necessarily smooth, simultaneously with initial temperatures in parabolic equations with dynamic boundary conditions. We prove a Lipschitz stability…

In this paper, we study the null controllability of weakly degenerate coupled parabolic systems with two different diffusion coefficients and one control force. To obtain this aim, we develop first new global Carleman estimates for…

In this article, We investigate an inverse problem of determining the time-dependent source factor in parabolic integro-differential equations from boundary data. We establish the uniqueness and the conditional stability estimate of…

For an inverse coefficient problem of determining a state-varying factor in the corresponding Hamiltonian for a mean field game system, we prove the global Lipschitz stability by spatial data of one component and interior data in an…