70 citations · 264 across the 36 of their papers we have counts for
26 papers · 1 filter
Inverse coefficient problems for one-dimensional time-fractional diffusion equations
Oleg Imanuvilov, Kazufumi Ito, Masahiro Yamamoto
We prove the uniqueness in determining a spatially varying zeroth-order coefficient of a one-dimensional time-fractional diffusion equation by initial value and Cauchy data at one…
One-dimensional coefficient inverse problems by transformation operators
Oleg Imanuvilov, Masahiro Yamamoto
We prove the uniqueness for an inverse problem of determining a matrix coefficient of a system of evolution equations $σ\ppp_t u = \ppp_x^2 u(t,x) - P(x) u(t,x)$ for $0<x<\e…
Determination of source terms and coefficients dependent on spatial variable of parabolic and Schrödinger equations
Oleg Imanuvilov, Masahiro Yamamoto
We establish the uniqueness in the determination of a source term or a coefficient of the zeroth order term of a second-order parabolic equation. Moreover we consider the determina…
Lipschitz stability for determination of states and inverse source problem for the mean field game equations
Oleg Imanuvilov, Hongyu Liu, Masahiro Yamamoto
In a bounded domain over time interval , we consider mean field game equations whose principal coefficients depend on the time and state variables wi…
Global Lipschitz stability for an inverse coefficient problem for a mean field game system
Oleg Imanuvilov, Masahiro Yamamoto
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 s…
Inverse parabolic problem with initial data by a single measurement
Oleg Y. Imanuvilov, M. Yamamoto
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…
Unique continuation for a mean field game system
Oleg Imanuvilov, Hongyu Liu, Masahiro Yamamoto
For a mean field game system, we prove the unique continuation which asserts that if Cauchy data are zero on arbitrarily chosen lateral subboundary, then the solution identically v…
Lipschitz stability for determination of states and inverse source problem for the mean field game equations
Oleg Imanuvilov, Hongyu Liu, Masahiro Yamamoto
We consider solutions satisfying the zero Neumann boundary condition and a linearized mean field game equation in whose principal coefficients depend on the time an…
Determination of a source term in Schrödinger equation with a data taken at final moment of observation
O. Y. Imanuvilov, M. Yamamoto
We establish the Lipshitz stability estimate in inverse problem of determination of a source term or zero order term in the Schrödinger equation with time-dependent coefficients un…
Sharp uniqueness and stability of solution for an inverse source problem for the Schrödinger equation
Oleg Imanuvilov, M. Yamamoto
The manuscript is concerned with uniqueness and stability for inverse source problem of determining spatially varying factor of a source term given by with suitab…
Inverse parabolic problems by Carleman estimates with data taken initial or final time moment of observation
O. Imanuvilov, M. Yamamoto
We consider a parabolic equation in a bounded domain $\OOO$ over a time interval with the homogeneous Neumann boundary condition. We arbitrarily choose a subboundary $Γ\sub…
Global Lipschitz stability for an inverse source problem for the Navier-Stokes equations
O. Y. Imanuvilov, M. Yamamoto
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…
Inverse source problem and the continuation for a fourth-order parabolic equation in general dimensions
O. Yu. Imanuvilov, M. Yamamoto
In this article, for a fourth-order parabolic equation which is closely related for example to the Cahn-Hilliard equation, we study an inverse source problem by interior data and t…
Inverse parabolic problems of determining functions with one spatial-component independence by Carleman estimate
Oleg Yu. Imanuvilov, Yavar Kian, Masahiro Yamamoto
For an initial-boundary value problem for a parabolic equation in the spatial variable and time , we consider an inverse problem of determining a coefficient w…
Stability for inverse source problems by Carleman estimates
X. Huang, O. Yu. Imanuvilov, M. Yamamoto
In this article, we provide a modified argument for proving conditional stability for inverse problems of determining spatially varying functions in evolution equations by Carleman…
Carleman estimate and an inverse source problem for the Kelvin-Voigt model for viscoelasticity
O. Y. Imanuvilov, M. Yamamoto
We consider the Kelvin-Voigt model for the viscoelasticity, and prove a Carleman estimate for functions without compact supports. Then we apply the Carleman estimate to prove the L…
Carleman estimate for linear viscoelasticity equations and an inverse source problem
Oleg Imanuvilov, Masahiro Yamamoto
We consider the linear system of viscoelasticity with the homogeneous Dirichlet boundary condition. First we prove a Carleman estimate with boundary values of solutions of viscoela…
Carleman estimate for the Navier-Stokes equations and an application to a lateral Cauchy problem
Mourad Bellassoued, Oleg Imanuvilov, Masahiro Yamamoto
We consider the nonstationary linearized Navier-Stokes equations in a bounded domain and first we prove a Carleman estimate with a regular weight function. Second we apply the Carl…
Stability and uniqueness for a two-dimensional inverse boundary value problem for less regular potentials
E. Blåsten, O. Yu. Imanuvilov, M. Yamamoto
We consider inverse boundary value problems for the Schrodinger equations in two dimensions. Within less regular classes of potentials, we establish a conditional stability estimat…
Uniqueness in inverse boundary value problems for fractional diffusion equations
Zhiyuan Li, O. Y. Imanuvilov, Masahiro Yamamoto
We consider an inverse boundary value problem for diffusion equations with multiple fractional time derivatives. We prove the uniqueness in determining a number of fractional time-…
Global uniqueness in inverse boundary value problems for Navier-Stokes equations and Lamé system in two dimensions
O. Yu. Imanuvilov, M. Yamamoto
We consider inverse boundary value problems for the Navier-Stokes equations and the isotropic Lamé system in two dimensions. The uniqueness without any smallness assumptions on unk…
Inverse problem by Cauchy data on arbitrary subboundary for system of elliptic equations
Oleg Imanuvilov, Masahiro Yamamoto
We consider an inverse problem of determining coefficient matrices in an -system of second-order elliptic equations in a bounded two dimensional domain by a set of Cauchy data o…
Inverse boundary value problem for Schrödinger equation in two dimensions
Oleg Imanuvilov, Masahiro Yamamoto
We relax the regularity condition on potentials of the Schrödinger equation in uniqueness results on the inverse boundary value problem which were recently proved in [11] and [5].
Partial Cauchy Data for General Second-Order Elliptic Operators in Two Dimensions
O. Imanuvilov, G. Uhlmann, M. Yamamoto
We consider the inverse problem of determining the coefficients of a general second-order elliptic operator in two dimensions by measuring the corresponding Cauchy data on an arbit…