Related papers: Fundamental solution and diffusion limits for the …
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 give an explicit representation of the fundamental solution to the heat equation on a half-space of ${\mathbb R}^N$ with the homogeneous dynamical boundary condition, and obtain upper and lower estimates of the fundamental solution.…
We study the heat equation on a half-space or on an exterior domain with a linear dynamical boundary condition. Our main aim is to establish the rate of convergence to solutions of the Laplace equation with the same dynamical boundary…
We study the heat equation in the exterior of the unit ball with a linear dynamical boundary condition. Our main aim is to find upper and lower bounds for the rate of convergence to solutions of the Laplace equation with the same dynamical…
We obtain necessary conditions and sufficient conditions for the solvability of the heat equation in a half-space of ${\bf R}^N$ with a nonlinear boundary condition. Furthermore, we study the relationship between the life span of the…
We study the diffusion (or heat) equation on a finite 1-dimensional spatial domain, but we replace one of the boundary conditions with a "nonlocal condition", through which we specify a weighted average of the solution over the spatial…
We study the linear heat equation on a halfspace with a linear dynamical boundary condition. We are interested in an appropriate choice of the function space of initial functions such that the problem possesses a solution. It was known…
This paper discusses finite time extinction for a perturbed fast diffusion equation with dynamic boundary conditions. The fast diffusion equation has the characteristic property of decay, such as the solution decays to zero in a finite…
In this paper, the initial and boundary problem of the difference equation which is a discretization of the semi-linear heat equation. The difference equation derived by discretizing the semi-linear heat equation has solutions which show…
By a probabilistic method we provide an explicit fundamental solution of the Cauchy problem associated to the heat equation on the half-line with constant drift and Dirichlet boundary condition at zero.
We consider the Fokas method expression for the solution of the heat equation on the half line with Dirichlet data and we study in detail its boundary behaviour near the spatiotemporal domain boundaries, i.e., the semi-axes, infinity and…
We investigate the fractional diffusion approximation of a kinetic equation in the upper-half plane with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…
We consider a family of initial boundary value problems governed by a fractional diffusion equation with Caputo derivative in time, where the parameter is the Newton heat transfer coefficient linked to the Robin condition on the boundary.…
In this paper we study the randomized heat equation with homogeneous boundary conditions. The diffusion coeffcient is assumed to be a random variable and the initial condition is treated as a stochastic process. The solution of this…
We study the well-posedness for initial boundary value problems associated with time fractional diffusion equations with non-homogenous boundary and initial values. We consider both weak and strong solutions for the problems. For weak…
Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori…
We consider a particle living in $\mathbb{R}_+$, whose velocity is a positive recurrent diffusion with heavy-tailed invariant distribution when the particle lives in $(0,\infty)$. When it hits the boundary $x=0$, the particle restarts with…
We investigate the fractional diffusion approximation of a kinetic equation set in a bounded interval with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…
This paper considers the initial-boundary value problem for the heat equation with a dynamic type boundary condition. Under some regularity, consistency and orthogonality conditions, the existence, uniqueness and continuous dependence upon…
In this paper, we consider the initial-boundary value problem of the 3D primitive equations for oceanic and atmospheric dynamics with only horizontal diffusion in the temperature equation. Global well-posedness of strong solutions are…