相关论文: Regularized Reconstruction of Scalar Parameters in…

The aim of this paper is to study the recovery of a spatially dependent potential in a (sub)diffusion equation from overposed final time data. We construct a monotone operator one of whose fixed points is the unknown potential. The…

This paper is concerned with backward problem for nonlinear space fractional diffusion with additive noise on the right-hand side and the final value. To regularize the instable solution, we develop some new regularized method for solving…

In this study, we focus on identifying solution and an unknown space-dependent coefficient in a space-time fractional differential equation by employing fractional Taylor series method. The substantial advantage of this method is that we…

This article is concerned with the inverse problem on determining the temporal component of the source term in a coupled system of time-fractional diffusion equations by single point observation. Under a non-degeneracy condition on the…

In this paper we study elliptic partial differential equations with rapidly varying diffusion coefficient that can be represented as a perturbation of a reference coefficient. We develop a numerical method for efficiently solving multiple…

We propose a technique for reformulation of state and parameter estimation problems as that of matching explicitly computable definite integrals with known kernels to data. The technique applies for a class of systems of nonlinear ordinary…

We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where…

We consider boundary value problems with Riemann-Liouville fractional derivatives of order $s\in (1, 2)$ with non-constant diffusion and reaction coefficients. A variational formulation is derived and analyzed leading to the well-posedness…

In this paper, we consider the problem of distributed parameter estimation in sensor networks. Each sensor makes successive observations of an unknown $d$-dimensional parameter, which might be subject to Gaussian random noises. The sensors…

This paper studies the distributed adaptiveestimation problems for stochastic large regression modelswith an infinite number of parameters. By constructing a re-cursive local cost function, we propose a novel distributedrecursive least…

We investigate the regional gradient observability of fractional sub-diffusion equations involving the Caputo derivative. The problem consists of describing a method to find and recover the initial gradient vector in the desired region,…

In many recent applications when new materials and technologies are developed it is important to describe and simulate new nonlinear and nonlocal diffusion transport processes. A general class of such models deals with nonlocal fractional…

We consider second-order functional differential operators with a constant delay. Properties of their spectral characteristics are obtained and a nonlinear inverse problem is studied, which consists in recovering the operators from their…

Nonlinear parametric inverse problems appear in many applications and are typically very expensive to solve, especially if they involve many measurements. These problems pose huge computational challenges as evaluating the objective…

A time-stepping L1 scheme for subdiffusion equation with a Riemann--Liouville time-fractional derivative is developed and analyzed. This is the first paper to show that the L1 scheme for the model problem under consideration is second-order…

We consider difference schemes for the time-fractional diffusion equation with variable coefficients and nonlocal boundary conditions containing real parameters $\alpha$, $\beta$ and $\gamma$. By the method of energy inequalities, for the…

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…

We study an inverse problem for fractional elasticity. In analogy to the classical problem of linear elasticity, we consider the unique recovery of the Lam\'e parameters associated to a linear, isotropic fractional elasticity operator from…

This paper studies linear reconstruction of partially observed functional data which are recorded on a discrete grid. We propose a novel estimation approach based on approximate factor models with increasing rank taking into account…

Conditional stability estimates allow us to characterize the degree of ill-posedness of many inverse problems, but without further assumptions they are not sufficient for the stable solution in the presence of data perturbations. We here…