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Nonlocal approximation of nonlinear diffusion equations
We show that degenerate nonlinear diffusion equations can be asymptotically obtained as a limit from a class of nonlocal partial differential...
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Global Existence of Smooth Solutions for the Diffusion Approximation Model of General Gas in Radiation Hydrodynamics
In this paper, we consider the 3-D Cauchy problem for the diffusion approximation model in radiation hydrodynamics. The existence and uniqueness of...
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A reaction–diffusion approximation of a semilinear wave equation with dam**
A reaction–diffusion approximation is a method that solutions of multi-component reaction–diffusion systems approximate those of differential...
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Diffusion approximation of critical controlled multi-type branching processes
Branching processes form an important family of stochastic processes that have been successfully applied in many fields. In this paper, we focus our...
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Explicit Approximation of Invariant Measure for Stochastic Delay Differential Equations with the Nonlinear Diffusion Term
To our knowledge, existing measure approximation theory requires the diffusion term of the stochastic delay differential equations (SDDEs) to be...
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Universal approximation property of a continuous neural network based on a nonlinear diffusion equation
Recently, differential equation-based neural networks have been actively studied. This paper discusses the universal approximation property of a...
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Iterative Weak Approximation and Hard Bounds for Switching Diffusion
We establish a novel convergent iteration framework for a weak approximation of general switching diffusion. The key theoretical basis of the...
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Approximation of the Subdiffusion Equation with Solution-dependent Fractional Time Derivative and Diffusion Coefficient
AbstractWe consider a boundary value problem for a nonlinear subdiffusion equation with Caputo fractional time derivative of the order
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A fast uniformly accurate global numerical approximation to solution and scaled derivative of system of singularly perturbed problems with multiple diffusion parameters on generalized adaptive mesh
The aim of this article is to analyze a robust numerical approximation to the solution along with the scaled first derivative (physically known as diff...
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An efficient approximation to the stochastic Allen-Cahn equation with random diffusion coefficient field and multiplicative noise
This paper studies the stochastic Allen-Cahn equation involving random diffusion coefficient field and multiplicative force noise. A new...
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The Diffusion Equation
The diffusion equation appears in many applications in science and engineering, and computational physiology is no exception. In its most basic form,...
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Finite Difference Approximation for the Space-Time Fractional Linear Diffusion Equation Involving the Caputo-Hadamard Fractional Derivative
In this paper, we provide an accurate numerical solution for space-time fractional linear diffusion equation involving the fractinal Caputo-Hadamard...
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On Numerical Approximation of Diffusion Problems Governed by Variable-Exponent Nonlinear Elliptic Operators
We highlight the interest and the limitations of the L 1 -based Young measure technique for studying convergence of numerical approximations for...
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On One Numerical Scheme for Solving Radiative Transfer Equations in the Diffusion Approximation
AbstractThe article presents a numerical technique for solving equations that describe the process of radiative transfer in protostellar disks. The...
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Analysis of an unsteady triple diffusion through quadratic Boussinesq approximation from a rotating cone in a rotating fluid
The objective of current communication is to explore the triple diffusive mixed flow with the fluid rotation on a rotating cone in an unsteady...
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Approximation of the Heat Fluxes Dynamics in the North Atlantic by Stochastic Diffusion Process
AbstractThe observational data for 1979–2018 in the North Atlantic region are analyzed. The dataset contains gridded various information about the...
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Diffusion approximation for a simple kinetic model with asymmetric interface
We study a diffusion approximation for a model of stochastic motion of a particle in one spatial dimension. The velocity of the particle is constant...
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Structure Preserving Finite Volume Approximation of Cross-Diffusion Systems Coupled by a Free Interface
We propose a two-point flux approximation finite-volume scheme for the approximation of two cross-diffusion systems coupled by a free interface to...
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A Multipoint Flux Approximation with a Diamond Stencil and a Non-Linear Defect Correction Strategy for the Numerical Solution of Steady State Diffusion Problems in Heterogeneous and Anisotropic Media Satisfying the Discrete Maximum Principle
In the present paper, we solve the steady state diffusion equation in 3D domains by means of a cell-centered finite volume method that uses a...
