Related papers: Darcy's problem coupled with the heat equation und…

Integro-partial differential equations occur in many contexts in mathematical physics. Typical examples include time-dependent diffusion equations containing a parameter (e.g., the temperature) that depends on integrals of the unknown…

This paper presents a mathematically exact self-similar solution to the joint nonsteady problems of vapour diffusion towards a droplet growing in a vapour-gas medium and of removal of heat released by a droplet into a vapour-gas medium…

We study a fully discrete finite element approximation of a model for unsteady flows of rate-type viscoelastic fluids with stress diffusion in two and three dimensions. The model consists of the incompressible Navier--Stokes equation for…

We develop estimates for the solutions and derive existence and uniqueness results of various local boundary value problems for Dirac equations that improve all relevant results known in the literature. With these estimates at hand, we…

We consider the stabilization problem on a manifold with boundary for a wave equation with measure-valued linear damping. For a wide class of measures, containing Dirac masses on hypersurfaces as well as measures with fractal support, we…

In this work, we study the gradient discretisation method (GDM) of the time-dependent Navier-Stokes equations coupled with the heat equation, where the viscosity depends on the temperature. We design the discrete method and prove its…

In this paper we study the influence of the Hardy potential in the fractional heat equation. In particular, we consider the problem $$(P_\theta)\quad \left\{ \begin{array}{rcl} u_t+(-\Delta)^{s} u&=&\l\dfrac{\,u}{|x|^{2s}}+\theta u^p+ c…

This paper is devoted to the homogenization of the heat conduction equation, with a homogeneous Dirichlet boundary condition, having a periodically oscillating thermal conductivity and a vanishing volumetric heat capacity. A homogenization…

The thermal and statistical properties of hadronic matter under some extreme conditions are investigated using an exactly solvable canonical ensemble model. A unified model describing both the fragmentation of nuclei and the thermal…

The convective transport in a multicomponent isothermal compressible fluid subject to the mass continuity equations is considered. The velocity is proportional to the negative pressure gradient, according to Darcy's law, and the pressure is…

We consider a numerical approximation of a linear quadratic control problem constrained by the stochastic heat equation with non-homogeneous Neumann boundary conditions. This involves a combination of distributed and boundary control, as…

We present and analyze a cut finite element method for the weak imposition of the Neumann boundary conditions of the Darcy problem. The Raviart-Thomas mixed element on both triangular and quadrilateral meshes is considered. Our method is…

A finite element approach to the elastic flow of a curve coupled with a diffusion equation on the curve is analysed. Considering the graph case, the problem is weakly formulated and approximated with continuous linear finite elements, which…

Application of finite element method and heat conductivity transfer model for calculation of temperature distribution in receiver for dish-Stirling concentrating solar system is described. The method yields discretized equations that are…

We solve the one-dimensional Dirac equation by taking into account the possibility of position-dependence in the mass function. We also take the Fermi velocity to act as a local variable and examine the combined effects of the two on the…

The goal of this paper is to prove a uniqueness result for a stochastic heat equation with a randomly perturbed potential, which can be considered as a variant of Hardy's uncertainty principle for stochastic heat evolutions.

It is up to now a challenge to control the conduction of heat. Here we develop a method to distort the temperature distribution signature of an object at will. As a result, the object accurately exhibits the same temperature distribution…

We prove that there exists a~large-data and global-in-time weak solution to a~system of partial differential equations describing an unsteady flow of an incompressible heat-conducting rate-type viscoelastic stress-diffusive fluid filling up…

We consider the Cauchy problem for heat equation with fractional Laplacian and exponential nonlinearity. We establish local well-posedness result in Orlicz spaces. We derive the existence of global solutions for small initial data. We…

We propose to analyse the discretization of the Stokes problem with nonconforming finite elements in light of the T-coercivity (cf. [1] for Helmholtz-like problems, see [2], [3] and [4] for the neutron diffusion equation). We propose…