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We study an inverse boundary value problem on the determination of principal order coefficients in isotropic nonautonomous heat flows stated as follows; given a medium, and in the absence of heat sources and sinks, can the time-dependent…
In this paper, we investigate direct and inverse problems for the time-fractional heat equation with a time-dependent leading coefficient for positive operators. First, we consider the direct problem, and the unique existence of the…
In this paper considering quantum heat transport equation (QHT) formulated in our earlier papers the temperature for universes with G < 0 is calculated. As the solution of complex QHT (Schrodinger type equation), the temperature is complex…
We consider the non-classical heat conduction equation, in the domain $D=\br^{n-1}\times\br^{+}$, for which the internal energy supply depends on an integral function in the time variable of % $(y , t)\mapsto \int_{0}^{t} u_{x}(0 , y , s)…
This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal data. This theory finds applications in multi-wave imaging, greedy methods to…
An exact analytical description of the internal radiative field inside an emitting-absorbing gray semi-transparent medium enclosed in a two-dimensional parallelogram cavity is proposed. The expressions of the incident radiation and the…
We derive the frequency-resolved heat current expression in the linear response regime for a setup comprised of reservoir, interacting central site, and tunneling barrier under the action of a time dependent electrical signal. We exploit…
In a domain of the Euclidean space, we estimate from below the distance to the boundary of global maximum points of solutions of elliptic and parabolic equations with homogeneous Dirichlet boundary values. As reference cases, we first…
We study a second-order parabolic equation with divergence form elliptic operator, having piecewise constant diffusion coefficients with two points of discontinuity. Such partial differential equations appear in the modelization of…
We present a fast adaptive method for the evaluation of heat potentials, which plays a key role in the integral equation approach for the solution of the heat equation, especially in a non-stationary domain. The algorithm utilizes a…
In this paper, we develop a factorization method to reconstruct cavities in a heat conductor by knowing the Neumann-to-Dirichlet map at the boundary of this conductor. The factorization method is a very well known reconstruction method for…
This paper considers one-dimensional heat transfer in a media with temperature-dependent thermal conductivity. To model the transient behavior of the system, we solve numerically the one-dimensional unsteady heat conduction equation with…
We consider the inverse problem of reconstructing the interior boundary curve of a doubly connected domain from the knowledge of the temperature and the thermal flux on the exterior boundary curve. The use of the Laguerre transform in time…
The two-dimensional flow of viscous incompressible liquid in a square cavity with a free boundary and differentially heated vertical sides is considered in the present work. The influence of gravitational and thermocapillary convection on…
Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order…
The divergence of the thermal conductivity in the thermodynamic limit is thoroughly investigated. The divergence law is consistently determined with two different numerical approaches based on equilibrium and non-equilibrium simulations. A…
The propagation of heat and thermal signals in the form of travelling waves is investigated for a nonlinear Maxwell-Cattaneo-Vernotte equation. The exact wave solutions are derived by expressing the thermal conductivity and the relaxation…
The paper deals with some problems related to recovering information about an obstacle in an Euclidean space from certain measurements of lengths of generalized geodesics in the exterior of the obstacle. The main result is that if two…
We consider the volume potential associated with the heat operator and we prove a mapping property in the space of distributions which are the time derivative of H\"older continuous functions. As an application we solve the Dirichlet and…
It is necessary to use more general models than the classical Fourier heat conduction law to describe small-scale thermal conductivity processes. The effects of heat flow memory and heat capacity memory (internal energy) in solids are…