Related papers: Initial-Boundary Value Problem for the heat equati…
Variational Quantum Eigensolver (VQE) is widely used in near-term hardware. However, their performances remain limited by the poor trainability and are dependent on random parameter initialization. In this work, we propose a warm start…
This paper focuses on the numerical solution of a dual-phase-lag heat conduction equation on a space unbounded domain. First, based on the Laplace transform and the Pad\'e approximation, a high-order local artificial boundary condition is…
We consider boundary value problems of the first and third kind for the diffusionwave equation. By using the method of energy inequalities, we find a priori estimates for the solutions of these boundary value problems.
Recently, gradient-based discrete sampling has emerged as a highly efficient, general-purpose solver for various combinatorial optimization (CO) problems, achieving performance comparable to or surpassing the popular data-driven approaches.…
A heat exchanger can be modeled as a closed domain containing an incompressible fluid. The moving fluid has a temperature distribution obeying the advection-diffusion equation, with zero temperature boundary conditions at the walls.…
We consider the initial boundary problem of 2D non-homogeneous incompressible heat conducting Navier-Stokes equations with vacuum, where the viscosity and heat conductivity depend on temperature in a power law of Chapman-Enskog. We derive…
We present an efficient sampling method for computing a partition function and accelerating configuration sampling. The method performs a random walk in the $\lambda$ space, with $\lambda$ being any thermodynamic variable that characterizes…
We introduce a time-implicit, finite-element based space-time discretization scheme for the backward stochastic heat equation, and for the forward-backward stochastic heat equation from stochastic optimal control, and prove strong rates of…
In this paper we consider the " exterior approach " to solve the inverse obstacle problem for the heat equation. This iterated approach is based on a quasi-reversibility method to compute the solution from the Cauchy data while a simple…
We study the equations of motion for a barotropic fluid in spherical symmetric flow. Making use of the Riemann invariants we consider the characteristic form of these equations. In a first part, we show that the resulting constraint…
A Neural Network (NN) based numerical method is formulated and implemented for solving Boundary Value Problems (BVPs) and numerical results are presented to validate this method by solving Laplace equation with Dirichlet boundary condition…
Due to the space and time dependence of the wave function in the time dependent Schroedinger equation, different boundary conditions are possible. The equation is usually solved as an ``initial value problem'', by fixing the value of the…
We consider the inverse acoustic obstacle problem for sound-soft star-shaped obstacles in two dimensions wherein the boundary of the obstacle is determined from measurements of the scattered field at a collection of receivers outside the…
This work presents global random walk approximations of solutions to one-dimensional Stefan-type moving-boundary problems. We are particularly interested in the case when the moving boundary is driven by an explicit representation of its…
In this paper, we present a general approach to obtain numerical schemes with good mesh properties for problems with moving boundaries, that is for evolving submanifolds with boundaries. This includes moving domains and surfaces with…
Taking into account the asymptotic behavior of some Wright functions and the existence of bounds for the Mainardi and the Wright function $W(-x,\frac{\alpha}{2}, 1)$ in $\mathbb{R}^+$ , three different initial-boundary-value problems for…
The Stochastic Heat Flow (SHF) emerges as the scaling limit of directed polymers in random environments and the noise-mollified Stochastic Heat Equation (SHE), specifically at the critical dimension of two and near the critical temperature.…
This work deals with the problem of choosing a time step for the numerical solution of boundary value problems for parabolic equations. The problem solution is derived using the fully implicit scheme, whereas a time step is selected via…
We consider random walks in a balanced i.i.d. random environment in $Z^d$ for $d\ge2$ and the corresponding discrete non-divergence form difference operators. We first obtain an exponential integrability of the heat kernel bounds. We then…
This paper investigates an inverse random source problem for stochastic evolution equations, including stochastic heat and wave equations, with the unknown source modeled as $g(x)f(t)\dot{W}(t)$. The research commences with the…