Related papers: Detection of time-varying heat sources using an an…
In this paper we explore the weak solution of a time-dependent inverse source problem and inverse initial problem for $q$-analogue of the heat equation. As an over-determination condition we have used integral type condition on…
We solve an inverse problem for the one-dimensional heat diffusion equation. We reconstruct the heat source function for the three types of data: 1) single position point and different times, 2) constant time and uniformly distributed…
This paper delves into the Inverse Stefan problem, specifically focusing on determining the time-dependent source coefficient in the parabolic heat equation governing heat transfer in a semi-infinite rod. The problem entails the intricate…
We introduce a numerical workflow to model and simulate transient close-contact melting processes based on the space-time finite element method. That is, we aim at computing the velocity at which a forced heat source melts through a…
This study presents fast and accurate analytical methods for transient thermal modeling in multi-layer composites with an arbitrary number of layers. The proposed approach accounts for internal heat generation and non-homogeneities in the…
We investigate an iterative mean value method for the inverse (and highly ill-posed) problem of solving the heat equation backwards in time. Semi-group theory is used to rewrite the solution of the inverse problem as the solution of a fixed…
This study focuses on addressing the inverse source problem associated with the parabolic equation. We rely on sparse boundary flux data as our measurements, which are acquired from a restricted section of the boundary. While it has been…
An inverse problem for a stationary heat transfer process is studied for a totally isolated bar on its lateral surface, of negligible diameter, made up of two consecutive sections of different, isotropic and homogeneous materials. At the…
We investigate an inverse source problem of the time-harmonic elastic wave equation. Some novel sampling-type numerical schemes are proposed to identify the moment tensor point sources in the Lam\'e system from near-field measurements.…
We introduce a new numerical method for solving time-harmonic acoustic scattering problems. The main focus is on plane waves scattered by smoothly varying material inhomogeneities. The proposed method works for any frequency $\omega$, but…
A one-phase Stefan problem for a semi-infinite material is investigated for special functional forms of the thermal conductivity and specific heat depending on the temperature of the phase-change material. Using the similarity…
Considering high-temperature heating, the equations of transient heat conduction model require an adaptation, i.e. the dependence of thermophysical parameters of the model on the temperature is to be identified for each specific material to…
In this work, we propose a Bayesian thinning algorithm for recovering weighted point source functions in the heat equation from boundary flux observations. The major challenge in the classical Bayesian framework lies in constructing…
Recent findings suggest that abnormal operating conditions of equipment in the oil and gas supply chain represent a large fraction of anthropogenic methane emissions. Thus, effective mitigation of emissions necessitates rapid identification…
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 data set descriptor introduces a structured, high-resolution dataset of transient thermal simulations for a vertical axis of a machine tool test rig. The data set includes temperature and heat flux values recorded at 29 probe locations…
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…
Urban areas are increasingly vulnerable to thermal extremes driven by rapid urbanization and climate change. Traditionally, thermal extremes have been monitored using Earth-observing satellites and numerical modeling frameworks. For…
In this work, a thermal energy transfer problem in a one-dimensional multilayer body is theoretically analyzed, considering diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, as well as…
Identification of abnormal source hidden in distributed parameter systems (DPSs) belongs to the category of inverse source problems. It is important in industrial applications but seldom studied. In this paper, we make the first attempt to…