Related papers: The Calder\'on problem for a nonlocal diffusion eq…

Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…

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 study the well-posedness of a semilinear fractional diffusion equation and formulate an associated inverse problem. We determine fractional power type nonlinearities from the exterior partial measurements of the Dirichlet-to-Neumann map.…

In the present paper, we study the Cauchy-Dirichlet problem to the nonlocal nonlinear diffusion equation with polynomial nonlinearities $$\mathcal{D}_{0|t}^{\alpha…

This paper is devoted to the inverse problem of determining the spatially dependent source in a time fractional diffusion-wave equation, with the aid of extra measurement data at subboundary. Uniqueness result is obtained by using the…

In this paper I consider the inverse boundary value problem for a quasilinear, anisotropic, elliptic equation of the form $\nabla\cdot(\gamma\nabla u+|\nabla u|^{p-2}\nabla u)=0$, where $\gamma$ is a smooth, matrix valued, function with a…

This article is concerned with an inverse problem of simultaneously determining a spatially varying coefficient and a Robin coefficient for a one-dimensional fractional diffusion equation with a time-fractional derivative of order…

We establish the uniqueness of semi-wavefront solution for a non-local delayed reaction-diffusion equation. This result is obtained by using a generalization of the Diekman-Kaper theory for a nonlinear convolution equation. Several…

This paper considers the Dirichlet problem $$ -\mathrm{div}(a\nabla u_a)=f \quad \hbox{on}\,\,\ D, \qquad u_a=0\quad \hbox{on}\,\,\partial D, $$ for a Lipschitz domain $D\subset \mathbb R^d$, where $a$ is a scalar diffusion function. For a…

We consider the inverse problem of determining a potential in a semilinear elliptic equation from the knowledge of the Dirichlet-to-Neumann map. For bounded Euclidean domains we prove that the potential is uniquely determined by the…

We consider the fractional anisotropic Calder\'on problem for the nonlocal parabolic equation $(\partial_t -\Delta_g)^s u=f$ ($0<s<1$) on closed Riemannian manifolds. More concretely, we can determine the Riemannian manifold $(M,g)$ up to…

We consider the inverse problem of determining the time independent scalar potential of the dynamic Schr\"odinger equation in an infinite cylindrical domain, from one Neumann boundary observation of the solution. Assuming that this…

The main purpose of this article is the study of an inverse problem for nonlocal porous medium equations (NPMEs) with a linear absorption term. More concretely, we show that under certain assumptions on the time-independent coefficients…

We consider a time-space fractional diffusion equation with a variable coefficient and investigate the inverse problem of reconstructing the source term, after regularizing the problem with the quasiboundary value method to mitigate the…

We outline an approach to the inverse problem of Calder\'on that highlights the role of microlocal normal forms and propagation of singularities and extends a number of earlier results also in the anisotropic case. The main result states…

We consider an inverse problem of determining the coefficients of a fractional $p\,$-Laplace equation in the exterior domain. Assuming suitable local regularity of the coefficients in the exterior domain, we offer an explicit reconstruction…

Variable order space-fractional diffusion equation derived as an important model to describe complex anomalous diffusion phenomenon. In this article, well-posedness theory has been constructed for equations with the "Dirichlet" or the…

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 prove an optimal stability estimate for Electrical Impedance Tomography with local data, in the case when the conductivity is precisely known on a neighborhood of the boundary. The main novelty here is that we provide a rather general…

We study the Lorentzian Calder\'on problem, where the objective is to determine a globally hyperbolic Lorentzian metric up to a boundary fixing diffeomorphism from boundary measurements given by the hyperbolic Dirichlet-to-Neumann map. This…