Related papers: Solving the heat equation with variable thermal co…
We consider a heat problem with discontinuous diffusion coefficientsand discontinuous transmission boundary conditions with a resistancecoefficient. For all compact $(\epsilon,\delta)$-domains $\Omega\subset\mathbb{R}^n$ with a $d$-set…
When the variations of surface temperature are measured both spatially and temporally, analytical expressions that correctly account for multi-dimensional transient conduction can be applied. To enhance the accessibility of these accurate…
In this paper, we study the flux identification problem for a nonlinear time-fractional viscoelastic equation with a general source function based on the boundary measurements. We prove that the direct problem is well-posed, i.e., the…
We describe a new form of diagonalization for linear two point constant coefficient differential operators with arbitrary linear boundary conditions. Although the diagonalization is in a weaker sense than that usually employed to solve…
The problem of a steady forced convection thermal boundary-layer past a flat plate with a prescribed surface heat flux is investigated both analytically and numerically. In view of the present formulation, the governing equations reduce to…
This work presents an alternative view on the numerical simulation of diffusion processes applied to the heat and moisture transfer through porous building materials. Traditionally, by using the finite-difference approach, the…
The paper addresses a two-temperature model for simulating compressible two-phase flow taking into account diffusion processes related to the heat conduction and viscosity of the phases. This model is reduced from the two-phase…
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 establish a unique continuation property for stochastic heat equations evolving in a bounded domain $G$. Our result shows that the value of the solution can be determined uniquely by means of its value on an arbitrary open subdomain of…
We introduce a novel explicit and stable numerical algorithm to solve the spatially discretized heat or diffusion equation. We compare the performance of the new method with analytical and numerical solutions. We show that the method is…
Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori…
A linear irreversible thermodynamic framework of heat conduction in rigid conductors is introduced. The deviation from local equilibrium is characterized by a single internal variable and a current intensity factor. A general constitutive…
We consider the homogeneous heat equation in a domain $\Omega$ in $\mathbb{R}^n$ with vanishing initial data and the Dirichlet boundary condition. We are looking for solutions in $W^{r,s}_{p,q}(\Omega\times(0,T))$, where $r < 2$, $s < 1$,…
There are various situations where the classical Fourier's law for heat conduction is not applicable, such as heat conduction in heterogeneous materials or for modeling low-temperature phenomena. In such cases, heat flux is not directly…
We show that, for certain evolution partial differential equations, the solution on a finite interval $(0,\ell)$ can be reconstructed as a superposition of restrictions to $(0,\ell)$ of solutions to two associated partial differential…
We study an inverse parabolic problem of identifying two source terms in heat equation with dynamic boundary conditions from a final time overdetermination data. Using a weak solution approach by Hasanov, the associated cost functional is…
Two methods based on Fourier series expansions (a Chandrasekhar functions-based method and a shifted Legendre polynomials -based method) are used to study analytically the eigenvalue problem governing the linear convection problem with an…
In this paper, we consider the heat-conducting compressible self-gravitating fluids in time-dependent domains, which typically describe the motion of viscous gaseous stars. The flow is governed by the 3-D Navier-Stokes-Fourier-Poisson…
We study the linear heat equation on a halfspace with a linear dynamical boundary condition. We are interested in an appropriate choice of the function space of initial functions such that the problem possesses a solution. It was known…
The kinetics of interfaces in alloy solidification pose a classic free boundary problem. This paper introduces an approach that amalgamates the distinctive characteristics of sharp and diffuse interface models. The motion of the diffuse…