The Steklov–Zaremba problem for the Laplace operator in a bounded domain with a strictly Lipschitz boundary is considered. A homogeneous Dirichlet condition is specified on the closed part of the boundary of the domain, and the Steklov boundary...
We recently proved that in our model of quantum gravity, the solutions to the quantized version of the full Einstein equations or to the Wheeler–DeWitt equation could be expressed as products of spatial and temporal eigenfunctions, or eigendist...
This paper studies the existence and uniqueness of the classical solution of inverse problems for a fourth-order hyperbolic equation with a complex-valued coefficient with Dirichlet and Neumann boundary conditions. Using the method of separation of v...
The paper investigates an algorithm for the numerical solution of a parametric eigenvalue problem for the Helmholtz equation on the plane specially tailored for the accurate mathematical modeling of lasing modes of microring lasers. The original prob...
Many dimensionality and model reduction techniques rely on estimating dominant eigenfunctions of associated dynamical operators from data. Important examples include the Koopman operator and its generator, but also the Schrödinger operator. We p...
In the present paper we study a class of Toeplitz operators called concentration operators that are self-adjoint and compact in the linear canonical Dunkl setting. We show that a finite vector space spanned by the first eigenfunctions of such operato...
The study focuses on reducing noise and nonstationary backgrounds in data collected through active infrared thermography (AIRT) for defect detection in materials. The authors employ adaptive fixed-rank kriging to analyze a sequence of thermograms obt...
In this paper, we promote the refinement method for estimating asymptotic expression of the fundamental solutions of a fourth order linear differential equation with discontinuous weight function and transmission conditions. These refinement solution...
Piezoelectric composites have found a wide range of applications in smart structures and devices and effective numerical methods should be developed to simulate not only the macroscopic coupled piezoelectric performances, but also the details of the...
This paper presents a novel methodology for estimating space- and time-dependent source terms in heat and mass diffusion problems. The approach combines classical integral transform techniques (CITTs) with the least squares optimization method, enabl...
An initial-boundary-value problem is considered for the one-dimensional diffusion equation with a general convolutional derivative in time and nonclassical boundary conditions. We are concerned with the inverse source problem of recovery of a space-d...
This article deals with a special case of the Sturm–Liouville boundary value problem (BVP), an eigenvalue problem characterized by the Sturm–Liouville differential operator with unknown spectra and the associated eigenfunctions. By examin...
In this paper, we consider a time fractional diffusion system with a nonlinear memory term in a bounded domain. We mainly prove some blow-up and global existence results for this problem. Moreover, we also give the decay estimates of the global solut...
Fourier spectral methods for solving some linear stochastic space-fractional partial differential equations perturbed by space-time white noises in the one-dimensional case are introduced and analysed. The space-fractional derivative is defined by us...
Motivated by mapping adverse artifactual events caused by body movements in electroencephalographic (EEG) signals, we present a functional independent component analysis based on the spectral decomposition of the kurtosis operator of a smoothed princ...
The meteorology data assimilation applications often encounter variational problems with unknown weights, where the corresponding Euler equation is an elliptic partial differential equation. This research focused on retrieving the weights in remote s...
The article presents results of an analytical and numerical modeling of electron fluid motion and heat generation in a rectangular conductor at an alternating electric potential. The analytical solution is based on the series expansion solution (Four...
In this paper, we continue to solve as accurately as possible singular eigenvalues problems attached to the Schrödinger equation. We use the conventional ChC and SiC as well as Chebfun. In order to quantify the accuracy of our outcomes, we use the dr...
In this paper, we consider a direct problem and an inverse problem involving a nonlinear fractional diffusion equation, which can be applied to many physical situations. The equation contains a Caputo fractional derivative, a symmetric uniformly elli...
A class of initial boundary value problems is here considered for a one-dimensional diffusion equation with a general time-fractional derivative with the Sonin kernel. One of the boundary conditions is in a general non-classical form, which includes...
The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective equations is the...
The present paper deals with the analytical evaluation of the hydrodynamic characteristics of an array of vertical axisymmetric bodies of arbitrary shape, placed in front of a reflecting vertical breakwater, which can be conceived as floaters for wav...
An estimation of the electric sources in the heart was conducted using a novel method, based on Huygens’ Principle, aiming at a direct estimation of equivalent bioelectric sources over the heart’s surface in real time. The main scope of this work was...
A nonlocal boundary value problem for the fractional version of the Rayleigh–Stokes equation, well-known in fluid dynamics, is studied. Namely, the condition
This paper investigates boundary value problems for a class of elliptic equations exhibiting uniform and non-uniform degeneracy, including cases of non-monotonic degeneration. A key objective is to identify conditions on the coefficients under which...
We consider a singularly perturbed boundary value problem
The exploration of gas pressure and its distribution in landfills is a principal concern for the design and management of municipal solid waste (MSW) landfills. A one-dimensional analytical model was proposed to simulate a vertical gas flow in a land...
Earlier quantum calculations of the optical response of Nakamura’s blue laser diode, assuming Kronig–Penney-like band-edge profiles, omitted the effects of charge polarization, cladding-layer asymmetry, and recombination delay times, whil...
The lithium-ion (Li-ion) battery is a promising energy storage technology for electronics, automobiles, and smart grids. Extensive research was conducted in the past to improve the prediction of the remaining capacity of the Li-ion battery. A robust...