Related papers: Initial-Boundary Value Problem for the heat equati…
We consider the initial boundary value problem of non-homogeneous stochastic heat equation. The derivative of the solution with respect to time receives heavy random perturbation. The space boundary is Lipschitz and we impose non-zero…
We establish essentially optimal bounds on the complexity of initial-value problems in the randomized and quantum settings. For this purpose we define a sequence of new algorithms whose error/cost properties improve from step to step. These…
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 consider the heat equation with spatially variable thermal conductivity and homogeneous Dirichlet boundary conditions. Using the Method of Fokas or Unified Transform Method, we derive solution representations as the limit of solutions of…
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…
This paper shows how the enclosure method which was originally introduced for elliptic equations can be applied to inverse initial boundary value problems for parabolic equations. For the purpose a prototype of inverse initial boundary…
This is a series of studies devoted to modeling and solving heat and mass transfer problems occurring in electric contacts where we employ and develop mathematical apparatus along with quantum algorithms for solving moving boundary value…
In this paper we develop an artificial initial boundary value problem for the high-order heat equation in a bounded domain $\Omega$. It is found an unique classical solution of this problem in an explicit form and shown that the solution of…
We approximate the white-noise driven stochastic heat equation by replacing the fractional Laplacian by the generator of a discrete time random walk on the one dimensional lattice, and approximating white noise by a collection of i.i.d.…
The following stochastic Cauchy initial-value problem is studied for the parabolic heat equation on a domain $ \mathbf{Q}\subset{\mathbf{R}}^{n}$ with random field initial data. \begin{align} &{\square}\widehat{u(x,t)} \equiv…
This paper considerers the problem of computing the value of a solution of the heat equation at a given point inside a bounded domain after the initial time. It is assumed that the initial value of the solution inside the domain (possibly…
We investigate the inverse problem of numerically identifying unknown initial temperatures in a heat equation with dynamic boundary conditions whenever some overdetermination data is provided after a final time. This is a backward parabolic…
This work presents an alternative view on the numerical simulation of diffusion processes applied to the heat and moisture transfer through porous building materials. Traditionally, by using the finite-difference approach, the…
This work deals with the one-dimensional Stefan problem with a general time-dependent boundary condition at the fixed boundary. Stochastic solutions are obtained using discrete random walks, and the results are compared with analytic…
A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…
We address the initial source identification problem for the heat equation, a notably ill-posed inverse problem characterized by exponential instability. Departing from classical Tikhonov regularization, we propose a novel approach based on…
We set up a framework for quantum stochastic thermodynamics based solely on experimentally controllable, but otherwise arbitrary interventions at discrete times. Using standard assumptions about the system-bath dynamics and insights from…
We consider the abstract initial value problem for the system of evolution equations which describe motion of micropolar fluids with heat conduction in a bounded domain. This problem has uniquely a mild solution locally in time for general…
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 introduce the walk-on-boundary (WoB) method for solving boundary value problems to computer graphics. WoB is a grid-free Monte Carlo solver for certain classes of second order partial differential equations. A similar Monte Carlo solver,…