Related papers: Uniqueness and regularization for unknown spacewis…
The problem of estimating the reaction coefficient of a system governed by a reaction-diffusion partial differential equation is tackled. An estimator relying on boundary measurements only is proposed. The estimator is based upon a setpoint…
From the final and interior temperature measurements identifying the source term with initial temperature simultaneously is an inverse heat conduction problem which is a kind of ill-posed. The optimal control framework has been found to be…
We investigate a convective Brinkman--Forchheimer problem coupled with a heat equation. The investigated model considers thermal diffusion and viscosity depending on the temperature. We prove the existence of a solution without restriction…
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 this paper we consider the solution of monotone inverse problems using the particular example of a parameter identification problem for a semilinear parabolic PDE. For the regularized solution of this problem, we introduce a total…
We study the one-dimensional stochastic heat equation with unbounded, nonlinear,Lipschitz coefficients with Dirichlet boundary conditions. Using Malliavin calculus, we construct a piecewise approximation of the solution u and establish…
Many applications in science and engineering require the solution of large linear discrete ill-posed problems that are obtained by the discretization of a Fredholm integral equation of the first kind in several space-dimensions. The matrix…
This work contributes in two areas, with sharp results, to the current investigation of regularity of solutions of heat equations (*) $Pu+\partial_tu=f$ on $\Omega\times I $, where $P$ is a nonlocal operator, and $\Omega \subset R^n$,…
Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute the…
We give the regularization for fractional integral by delta sequence and apply it to obtain existence-uniqueness theorems in Colombeau algebras for nonlinear equations with singularities: nonlinear system of integral equations with polar…
Numerical approximations to the solution of a linear singularly perturbed parabolic reaction-diffusion problem with incompatible bound\-ary-initial data are generated, The method involves combining the computational solution of a classical…
We prove the maximal local regularity of weak solutions to the parabolic problem associated with the fractional Laplacian with homogeneous Dirichlet boundary conditions on an arbitrary bounded open set $\Omega\subset\mathbb{R}^N$. Proofs…
We study the problem of identifying the parameters of a linear system from its response to multiple unknown waveforms. We assume that the system response is a scaled superposition of time-delayed and frequency-shifted versions of the…
The present paper analyzes a spectral regularization of a time-reversed reaction-diffusion problem with globally and locally Lipschitz nonlinearities. This type of inverse and ill-posed problems arises in a variety of real-world…
This paper investigates an inverse random source problem for stochastic evolution equations, including stochastic heat and wave equations, with the unknown source modeled as $g(x)f(t)\dot{W}(t)$. The research commences with the…
In this paper, we discuss the problem of system identification when frequency domain side information is available on the system. Initially, we consider the case where the prior knowledge is provided as being the $\Hcal_{\infty}$-norm of…
In this paper we investigate regularity aspects for solutions of the nonlinear parabolic equation $$ u_t= \Delta u^m, \quad m > 1 $$ usually called the porous medium equation. More precisely, we provide sharp regularity estimates for…
In the present paper we study inverse problems related to determining the time-dependent coefficient and unknown source function of fractional heat equations. Our approach shows that having just one set of data at an observation point…
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…
Nonlocal operators with integral kernels have become a popular tool for designing solution maps between function spaces, due to their efficiency in representing long-range dependence and the attractive feature of being resolution-invariant.…