Related papers: Functional solutions for problems of heat and mass…
This article presents a new approach to the dynamics of a particle system, divided into two distinct microstates spreading out in a homogeneous medium. The particles belonging to the main microstate spread according to classical Fick's law…
Almost nothing is known about the layer structure of solutions to singularly perturbed Caputo fractional boundary value problems. We discuss simple convection-diffusion and reaction-diffusion problems.
We consider a second order singularly perturbed boundary value problem, of reaction-convection-diffusion type with two small parameters, and the approximation of its solution by the $hp$ version of the Finite Element Method on the so-called…
The heat equation is considered in the complex system consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies a Newton-type boundary condition is imposed. An equation for the limiting…
In this paper, we mainly introduce a general method to study the existence and uniqueness of solution of free boundary problems with partially degenerate diffusion.
We consider a steady-state heat conduction problem $P$ for the Poisson equation with mixed boundary conditions in a bounded multidimensional domain $\Omega$. We also consider a family of problems $P_{\alpha}$ for the same Poisson equation…
Solutions of the Dirichlet and Robin boundary value problems for the multi-term variable-distributed order diffusion equation are studied. A priori estimates for the corresponding differential and difference problems are obtained by using…
In this paper, we study the Cauchy problem for a heat equation governed by a mixed local--nonlocal diffusion operator with spatially irregular coefficients. We first establish classical well-posedness in an energy framework for bounded,…
Mass transport problems are ubiquitous in diverse fields of physics and engineering. With the development of fractional calculus, many have taken to studying problems of fractional mass transport either through numerical simulations or…
From the viewpoint of operator theory, we deal with the temperature dependence of the solution to the BCS gap equation for superconductivity. When the potential is a positive constant, the BCS gap equation reduces to the simple gap…
We describe an exact and highly efficient numerical algorithm for solving a special but important class of convection-diffusion equations. These equations occur in many problems in physics, chemistry, or biology, and they are usually hard…
We discuss the problem of heat conduction in classical and quantum low dimensional systems from a microscopic point of view. At the classical level we provide convincing numerical evidence for the validity of Fourier law of heat conduction…
A new method is introduced for studying boundary value problems for a class of linear PDEs with {\it variable} coefficients. This method is based on ideas recently introduced by the author for the study of boundary value problems for PDEs…
Herein, we analyse polytropic processes for an ideal gas within the wider concept of thermal capacity. To answer the question of whether the thermal capacity is a process, path, or state function, we argue that it should be tentatively set…
It is shown that the solution maps of an abstract functional differential equations (FDEs) are $\alpha$-contractions in the phase space equipped with an equivalent norm under appropriate assumptions. This result can be applied to…
In this paper, we are interested in the study of a problem with fractional derivatives having boundary conditions of integral types. The problem represents a Caputo type advection-diffusion equation where the fractional order derivative…
The Ward identities for the charge and heat currents are derived for particle-particle and particle-hole pairs. They are the exact constraints on the current-vertex functions imposed by conservation laws and should be satisfied by…
We solve a class of BSDE with a power function $f(y) = y^q$, $q > 1$, driving its drift and with the terminal boundary condition $ \xi = \infty \cdot \mathbf{1}_{B(m,r)^c}$ (for which $q > 2$ is assumed) or $ \xi = \infty \cdot…
Convection-diffusion equations provide the basis for describing heat and mass transfer phenomena as well as processes of continuum mechanics. To handle flows in porous media, the fundamental issue is to model correctly the convective…
A fractional Stefan problem with a boundary convective condition is solved, where the fractional derivative of order $ \alpha \in (0,1) $ is taken in the Caputo sense. Then an equivalence with other two fractional Stefan problems (the first…