Related papers: Uniqueness and stability for inverse source proble…
We consider the inverse problem for the wave equation which consists of determining an unknown space-dependent force function acting on a vibrating structure from Cauchy boundary data. Since only boundary data are used as measurements, the…
The paper deals with reaction-diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. Such problems describe biological processes and chemical reactions in which diffusive and…
We consider the inverse problem of identification of degenerate diffusion coefficient of the form $x^\alpha a(x)$ in a one dimensional parabolic equation by some extra data. We first prove by energy methods the uniqueness and Lipschitz…
In this work we investigate an inverse coefficient problem for the one-dimensional subdiffusion model, which involves a Caputo fractional derivative in time. The inverse problem is to determine two coefficients and multiple parameters (the…
In this work, we consider an inverse problem of determining a source term for a structural acoustic partial differentia equation (PDE) model, comprised of a two or three-dimensional interior acoustic wave equation coupled to a Kirchoff…
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…
This paper is concerned with uniqueness in inverse acoustic scattering with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field…
This article is devoted to the simultaneous resolution of three inverse problems, among the most important formulation of inverse problems for partial differential equations, stated for some class of diffusion equations from a single…
We are concerned with the problem of determining the damping boundary coefficient appearing in a dissipative wave equation from a single boundary measurement. We prove that the uniqueness holds at the origin provided that the initial…
The diffusion system with time-fractional order derivative is of great importance mathematically due to the nonlocal property of the fractional order derivative, which can be applied to model the physical phenomena with memory effects. We…
We prove logarithmic stability in the parabolic inverse problem of determining the space-varying factor in the source, by a single partial boundary measurement of the solution to the heat equation in an infinite closed waveguide, with…
In the present work, we investigate a uniqueness of solution of the inverse source problem with non-local conditions for mixed parabolic-hyperbolic type equation with Caputo fractional derivative. Solution of the problem we represent as…
Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…
We study the increasing stability of an inverse source problem for the Helmholtz equation from limited-aperture far field data at multiple wave numbers. The measurement data are givenby the far field patterns $u^\infity(\hat{x},k)$ for all…
We study the inverse backscattering problem for time-dependent potentials. We prove uniqueness and Lipshitz stability for the recovery of small potentials.
In this work, we study an inverse problem of recovering a space-time dependent diffusion coefficient in the subdiffusion model from the distributed observation, where the mathematical model involves a Djrbashian-Caputo fractional derivative…
This paper investigates an inverse source problem for a multi-term time-fractional diffusion equation with Caputo derivatives. The source term is separable as \(f(x)g(t)\), with the unknown spatial component \(f(x)\) reconstructed from an…
We study increasing stability in the inverse source problems for the Helmholtz equation and the classical Lame system from (minimal) boundary data at multiple wave numbers. By using the Fourier transform with respect to wave numbers,…
This paper deals with the unique continuation of solutions for a one-dimensional anomalous diffusion equation with Caputo derivative of order $\alpha\in(0,1)$. Firstly, the uniqueness of solutions to a lateral Cauchy problem for the…
We consider the homogenization for time-fractional diffusion equations in a periodic structure and we derive the homogenized time-fractional diffusion equation. Then we discuss the determination of the constant diffusion coefficient by…