Related papers: On inverse problems arising in fractional elastici…
In this paper, we consider the indefinite fractional elliptic problem. A corresponding Liouville-type theorem for the indefinite fractional elliptic equations is established. Furthermore, we obtain a priori bound for solutions in a bounded…
We investigate the continuity of boundary operators, such as the Neumann-to-Dirichlet map, with respect to the coefficient matrices of the underlying elliptic equations. We show that for nonsmooth coefficients the correct notion of…
In this paper, we consider two linear inverse problems for the time-fractional wave equation, assuming that its right-hand side takes the separable form $f(t)h(x)$, where $t \geq 0$ and $x \in \Omega \subset R^N $. The objective is to…
This paper considers the robustness of an uncertain nonlinear system along a finite-horizon trajectory. The uncertain system is modeled as a connection of a nonlinear system and a perturbation. The analysis relies on three ingredients.…
We provide a general framework for fractional Hardy inequalities. Our framework covers, for instance, fractional inequalities related to the Dirichlet forms of some L\'evy processes, and weighted fractional inequalities on irregular open…
We initiate studying inverse spectral problems for Dirac-type functional-differential operators with constant delay. For simplicity, we restrict ourselves to the case when the delay parameter is not less than one half of the interval. For…
The Neumann problem of linear elasticity is singular with a kernel formed by the rigid motions of the body. There are several tricks that are commonly used to obtain a non-singular linear system. However, they often cause reduced accuracy…
In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic…
We determine the asymptotic behaviour of (bilateral) obstacle problems for fractional energies in rather general aperiodic settings via Gamma-convergence arguments. As further developments we consider obstacles with random sizes and shapes…
We consider a problem of quantitative static elastography, the estimation of the Lam\'e parameters from internal displacement field data. This problem is formulated as a nonlinear operator equation. To solve this equation, we investigate…
We investigate existence and uniqueness of solutions for a class of nonlinear nonlocal problems involving the fractional $p$-Laplacian operator and singular nonlinearities.
We study a nonlinear elliptic boundary value problem defined on a smooth bounded domain involving the fractional Laplace operator, a concave-convex powers term together with mixed Dirichlet-Neumann boundary conditions.
We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to…
The paper derived differential equations which solve the problem of restoration the motion parameters for a rigid reference frame from the known proper acceleration and angular velocity of its origin as functions of proper time. These…
Herein, we study an inverse problem for detecting unknown obstacles by the enclosure method using the Dirichlet--to--Neumann map for measurements. We justify the method for an penetrable obstacle case involving a biharmonic equation. We use…
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…
In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and…
Topological defects, such as disclination lines in nematic liquid crystals, are fundamental to many physical systems and applications. In this work, we study the behavior of nematic disclinations in thin parallel-plate geometries with…
This paper deals with the distributed order time-fractional diffusion equations with non-homogeneous Dirichlet (Nuemann) boundary condition. We first prove the wellposedness of the weak solution to the initial boundary value problem for the…
Consider two inverse problems for Sturm-Liouville problems on the unit interval. It means that there are two corresponding mappings $F, f$ from a Hilbert space of potentials $H$ into their spectral data. They are called isomorphic if $F$ is…