Related papers: Two analytical formulae of the temperature inside …
We solve a set of selected exercises on rotational motion requiring a mechanical and thermodynamical analysis. When non-conservative forces or thermal effects are present, a complete study must use the first law of thermodynamics together…
This work presents the derivation of a model for the heating process of the air of a glass dome, where an indoor swimming pool is located in the bottom of the dome. The problem can be reduced from a three dimensional to a two dimensional…
In this paper, we consider the inverse problem of determining the time-dependent source term in the general setting of Hilbert spaces and for general additional data. We prove the well-posedness of this inverse problem by reducing the…
An analytical procedure for calculating the critical temperature and estimating the size of critical region for a cell fluid model is developed. Our numerical calculations are illustrated by the case of the Morse potential parameters…
An initial-value problem for an ordinary differential equation of the first order, is considered. It is supposed that the right-hand side of the equation is a continuous function defined on a set consisting of an open set and a part of its…
We prove that the initial-value problem for the fractional heat equation admits a solution provided that the (possibly unbounded) initial datum has a conveniently moderate growth at infinity. Under the same growth condition we also prove…
Among the three heat conduction modes, the ballistic propagation is the most difficult to model. In the present paper, we discuss its physical interpretations and showing different alternatives to its modeling. We highlight two of them: a…
In his paper the heating of the fullerenes by ultra-short laser pulses is investigated. The thermal Heaviside equation is formulated and solved for the Cauchy initial condition The effective thermal relaxation time is calculated.. Key…
Let $\Omega$ be a two-dimensional heat conduction body. We consider the problem of determining the heat source $F(x,t)=\varphi(t)f(x,y)$ with $\varphi$ be given inexactly and $f$ be unknown. The problem is nonlinear and ill-posed. By a…
We show that a certain error estimate for a fully discrete finite element approximation of the solution of the heat equation which is defined in a two-dimensional Euclidean domain carries over to the case of a general linear parabolic…
In this paper we consider non-local (in time) heat equations on time-increasing parabolic sets whose boundary is determined by a suitable curve. We provide a notion of solution for these equations and we study well-posedness under Dirichlet…
Lie symmetry method is applied to find analytic solutions of initial-boundary-value problems of transient conduction in semi-infinite solid with constant surface temperature or constant heat flux condition. The solutions are obtained in a…
We consider necessary conditions and sufficient conditions on the solvability of the Cauchy--Dirichlet problem for a fractional semilinear heat equation in open sets (possibly unbounded and disconnected) with a smooth boundary. Our…
The energy efficiency of ice hockey arenas is a central concern for the administrations, as these buildings are well known to consume a large amount of energy. Since they are composite, complex systems, solutions to such a problem can be…
We consider a free boundary problem for the heat equation with a given non-negative external heat source. On the free boundary, we impose the zero Dirichlet condition and the fixed normal derivative so that heat escapes from the boundary.…
We present analytical formula along with its existence theorem for solution of inverse heat conduction problem of semi-infinite bar, equivalent to a Volterra integral equation of first kind, as an infinite series of fractional derivatives.…
In this paper, we study a two-point boundary value problem consisting of the heat equation on the open interval $(0,1)$ with boundary conditions which relate first and second spatial derivatives at the boundary points. Moreover, the unique…
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…
The reheating process in inflationary universe models is considered as an out-of-equilibrium mixture of two interacting and reacting fluids, and studied within the framework of causal, irreversible thermodynamics. The evolution of the…
Various sharp pointwise estimates for the gradient of solutions to the heat equation are obtained. The Dirichlet and Neumann conditions are prescribed on the boundary of a half-space. All data belong to the Lebesgue space $L^p$. Derivation…