Related papers: A convergent numerical method for a multi-frequenc…
In this paper, we study two types of inverse problems for space semi-discrete stochastic parabolic equations in arbitrary dimensions. The first problem concerns a semi-discrete inverse source problem, which involves determining the random…
We consider a two-component semilinear reaction-diffusion system in a bounded spatial domain $\Omega$ over a time interval $(0,T)$, which governs the water density $u(x,t)$ and the vegetation biomass density $v(x,t)$ for $x\in\Omega$ and…
We consider inverse boundary value problems for elliptic equations of second order of determining coefficients by Dirichlet-to-Neumann map on subboundaries, that is, the mapping from Dirichlet data supported on $\partial\Omega\setminus…
We consider inverse boundary value problems for the Jordan-Moore-Gibson-Thompson (JMGT) equation in nonlinear acoustics with quadratic nonlinearities of Kuznetsov-type and Westervelt-type. We show that the associated boundary…
We consider uniqueness in an inverse Schr\"odinger problem in a bounded domain in $\mathbb{R}^2$ given the Dirichlet-to-Neumann map on part of the boundary. On the remaining boundary we impose a new type of singular boundary condition with…
We introduced in [arXiv:1106.3204] a method to locate discontinuities of a wave speed in dimension two from acoustic boundary measuments modelled by the hyperbolic Neumann-to-Dirichlet operator. Here we extend the method for sound hard…
We extend the study of inverse boundary value problems to the setting of fully nonlinear PDEs by considering an inverse source problem for the Monge-Amp\`ere equation \[ \det D^2 u = F. \] We prove that, on a convex Euclidean domain in the…
In this paper we study the convergence of a finite volume approximation of a convective diffusive elliptic problem with Neumann boundary conditions and L 1 data. To deal with the non-coercive character of the equation and the low regularity…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
We are concerned with an inverse problem associated with the fractional Helmholtz system that arises from the study of viscoacoustics in geophysics and thermoviscous modelling of lossy media. We are particularly interested in the case that…
A novel perturbative method, proposed by Panda {\it et al.} [1] to solve the Helmholtz equation in two dimensions, is extended to three dimensions for general boundary surfaces. Although a few numerical works are available in the literature…
We consider the inverse multiphase Stefan problem with homogeneous Dirichlet boundary condition on a bounded Lipschitz domain, where the density of the heat source is unknown in addition to the temperature and the phase transition…
In this paper, we shall prove a Carleman estimate for the so-called Zaremba problem. Using some techniques of interpolation and spectral estimates, we deduce a result of stabilization for the wave equation by means of a linear Neumann…
The article [HPS] established a monotonicity inequality for the Helmholtz equation and presented applications to shape detection and local uniqueness in inverse boundary problems. The monotonicity inequality states that if two scattering…
It is by now well-known that one can recover a potential in the wave equation from the knowledge of the initial waves, the boundary data and the flux on a part of the boundary satisfying the Gamma-conditions of J.-L. Lions. We are…
The complex Helmholtz equation $(\Delta + k^2)u=f$ (where $k\in{\mathbb R},u(\cdot),f(\cdot)\in{\mathbb C}$) is a mainstay of computational wave simulation. Despite its apparent simplicity, efficient numerical methods are challenging to…
In the present work, we discuss a unique solvability of an inverse-source problem with integral transmitting condition for time-fractional mixed type equation in a rectangular domain, where the unknown source term depends on space variable…
An inverse problem of identifying locations and certain properties of small dielectric inhomogeneities in a homogeneous background medium from boundary measurements on a part of the boundary is studied. Using as weights particular…
Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…
In this paper, we consider the inverse problem of recovering a diffusion and absorption coefficients in steady-state optical tomography problem from the Neumann-to-Dirichlet map. We first prove a Global uniqueness and Lipschitz stability…