Related papers: Heat bullets
Inspired by the Galerkin and particular method, a new approximation approach is recalled in the Cartesian case. In this paper, we are interested specially by constructing this method, when the domain of consideration is a two dimensional…
By using the propagator of linear potential as a main tool, we extend the Airy gas model, originally developed for the three-dimensional ($d=3$) edge electron gas, to systems in reduced dimensions ($d=2,1$). First, we derive explicit…
Recently, Rissanen et al., (2022) have presented a new type of diffusion process for generative modeling based on heat dissipation, or blurring, as an alternative to isotropic Gaussian diffusion. Here, we show that blurring can equivalently…
We obtained a new representation of a solution of the heat conduction equation with boundary condition of the third kind for a layer. The result is presented as a superposition of fundamental solutions for an unbounded system with variable…
This paper is concerned with the spatio-temporal dynamics of nonnegative bounded entire solutions of some reaction-diffusion equations in R N in any space dimension N. The solutions are assumed to be localized in the past. Under certain…
We study the higher-order heat-type equation with first time and M-th spatial partial derivatives, M = 2, 3, ... . We demonstrate that its exact solutions for M even can be constructed with the help of signed Levy stable functions. For M…
Spatially accelerating beams that are solutions to the Maxwell equations may propagate along incomplete circular trajectories, after which diffraction broadening takes over and the beams spread out. Taking these truncated Bessel wave fields…
We present new electromagnetic plasma wavepacket solutions that propagates in one time and one space coordinates. Differently to the usual plane wave solution, which is written in terms of separation of variables, all our solutions are…
The three-dimensional incompressible Boussinesq system is one of the important equations in fluid dynamics. The system describes the motion of temperature-dependent incompressible flows. And the temperature naturally has diffusion.…
We derive diffusive macroscopic equations for the particle and energy density of a system whose time evolution is described by a kinetic equation for the one particle position and velocity function f(r,v,t) that consists of a part that…
We study the heat equation on a half-space with a linear dynamical boundary condition. Our main aim is to show that, if the diffusion coefficient tends to infinity, then the solutions converge (in a suitable sense) to solutions of the…
We solve the nonlocal convection equations. The solutions for four model problems are compared with results of GSPH simulations. In each case we test two closure schemes: 1) where third moments are defined by the diffusion approximation;…
In this paper, we study a system of thermoelasticity with a degenerated second order operator in the Heat equation. We analyze the evolution of the energy density of a family of solutions. We consider two cases: when the set of points where…
A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…
We formulate dynamical rate equations for physical processes driven by a combination of diffusive growth, size fragmentation and fragment coagulation. Initially, we consider processes where coagulation is absent. In this case we solve the…
An asymptotic limit of a class of Cahn-Hilliard systems is investigated to obtain a general nonlinear diffusion equation. The target diffusion equation may reproduce a number of well-known model equations: Stefan problem, porous media…
We construct an explicit solution of the Cauchy initial value problem for certain diffusion-type equations with variable coefficients on the entire real line. The corresponding Green function (heat kernel) is given in terms of elementary…
This article presents a theoretical analysis of a one-dimensional heat transfer problem in two layers involving diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, and heat generation due…
Heat conduction in three-dimensional nonlinear lattices is investigated using a particle dynamics simulation. The system is a simple three-dimensional extension of the Fermi-Pasta-Ulam $\beta$ (FPU-$\beta$) nonlinear lattices, in which the…
Classical and non classical Besov and Triebel-Lizorkin spaces with complete range of indices are developed in the general setting of Dirichlet space with a doubling measure and local scale-invariant Poincar\'e inequality. This leads to Heat…