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This paper is concerned with a new type of inverse obstacle problem governed by a variable-order time-fraction diffusion equation in a bounded domain. The unknown obstacle is a region where the space dependent variable-order of fractional…
The complete characterization of spatial coherence is difficult because the mutual coherence function is a complex-valued function of four independent variables. This difficulty limits the ability of controlling and optimizing spatial…
For the heat equation in a bounded domain we give a stability result for a smooth diffusion coefficient. The key ingredients are a global Carleman-type estimate, a Poincar\'e-type estimate and an energy estimate with a single observation…
The aim of this paper is to investigate the response of this system/scheme in terms of stability in presence of explicitly treated residual terms, as it inevitably occurs in the reality of NWP. This sudy is restricted to the impact of…
An inverse problem of finding an obstacle and the boundary condition on its surface from the fixed-energy scattering data is studied. A new method is developed for a proof of the uniqueness results. The method does not use the discreteness…
Inverse problem to determine simultaneously a general space- and time-dependent source and an initial state in a fractional diffusion equation from an {\it a posteriori} measurement of the normal derivative of the state on a portion of a…
We deal with an inverse problem arising in corrosion detection. We prove a stability estimate for a nonlinear term on the inaccessible portion of the boundary by electrostatic boundary measurements on the accessible one.
The incompressible smoothed particle hydrodynamics method (ISPH) is a numerical method widely used for accurately and efficiently solving flow problems with free surface effects. However, to date there has been little mathematical…
In this article, we investigate the determination of the spatial component in the time-dependent second order coefficient of a hyperbolic equation from both theoretical and numerical aspects. By the Carleman estimates for general hyperbolic…
We consider the identification of a nonlinear friction law in a one-dimensional damped wave equation from additional boundary measurements. Well-posedness of the governing semilinear hyperbolic system is established via semigroup theory and…
We investigate stability of both localized time-periodic coherent states (pulsons) and uniformly distributed coherent states (oscillating condensate) of a real scalar field satisfying the Klein-Gordon equation with a logarithmic…
In this article, we study the stability in the inverse problem of determining the time-dependent convection term and density coefficient appearing in the convection-diffusion equation, from partial boundary measurements. For dimension…
In the paper the conditions are obtained providing existence and uniqueness of the regular solution of the boundary problem for class of the second order homogeneous operator-differential equation with singular coefficients. High term of…
Necessary and sufficient conditions for the internal stability of formations whose dynamics are obtained is determined by linear differential equations.
We investigate the inverse problem consisting in the identification of constant coefficients for a fractional-in-time partial differential equation governed by a finite sum of positive self-adjoint operators on a Hilbert space under…
This letter announces and summarizes results obtained in arXiv:1111.5051 and considers several natural extensions. The aforementioned paper proposes a procedure to reconstruct coefficients in a second-order, scalar, elliptic equation from…
We study the invariant measure of the one-dimensional stochastic Allen-Cahn equation for a small noise strength and a large but finite system. We endow the system with inhomogeneous Dirichlet boundary conditions that enforce at least one…
A frame $(x_j)_{j\in J}$ for a Hilbert space $H$ is said to do phase retrieval if for all distinct vectors $x,y\in H$ the magnitude of the frame coefficients $(|\langle x, x_j\rangle|)_{j\in J}$ and $(|\langle y, x_j\rangle|)_{j\in J}$…
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…
We generalize many recent uniqueness results on the fractional Calder\'on problem to cover the cases of all domains with nonempty exterior. The highlight of our work is the characterization of uniqueness and nonuniqueness of partial data…