Two-dimensional boundary value problem of the diffusion
type: Item
instance of: scholarly article
title: Two-dimensional boundary value problem of the diffusion
zbMATH Open document ID: 0604.35032
author: Nguyen Van Gia
published in: Acta Mathematica Vietnamica
publication date: 1984-01-01T00:00:00Z
review text: The paper deals with a parabolic boundary value problem for the diffusion equation describing the concentration C(x,y;t) of suspended sediments in the domain (0,\(\infty)\times (0,H):\) \[ C_ t+U(x,y)C_ x=K_ 1(y)C_{xx}+(K_ 2(y)C_ y)_ y+VC_ y \] with an initial concentration at \(t=0\), prescribed time-dependent boundary values at \(x=0\), time-independent values at \(y=0\) and natural boundary conditions at \(y=H\). Under the assumption that \(K_ 2\) is constant asymptotic solutions are found; for a strictly increasing coefficient \(K_ 2\) estimates for the asymptotic solutions are given. In a simpler case of constant coefficients of the diffusion equation analytic and asymptotic solutions are found. Influences of the coefficients of the diffusion equation, the initial concentration and the boundary conditions on the asymptotic solutions are analysed.
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35C20
Mathematics Subject Classification ID: 35B30
zbMATH DE Number: 3975448
zbMATH Keywords: boundary value problem
zbMATH Keywords: diffusion
zbMATH Keywords: asymptotic solutions
zbMATH Keywords: coefficients
zbMATH Keywords: initial concentration
zbMATH Keywords: boundary conditions
reviewed by: J. Weisel
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3975448