Neumann problems for quasi-linear parabolic systems modeling polydisperse suspensions

Berres, S; Burger, R; Frid, H

Abstract

We discuss the well-posedness of a class of Neumann problems for n × n quasi-linear parabolic systems arising from models of sedimentation of polydisperse suspensions in engineering applications. This class of initial-boundary value problems includes the standard (zero-flux) Neumann condition in the limit as a positive perturbation parameter θ goes to 0. We call, in general, the problem associated with θ ≥ 0 the θ-flux Neumann problem. The Neumann boundary conditions, although natural and usually convenient for integration by parts, are nonlinear and couple the different components of the system. An important aspect of our analysis is a time stepping procedure that considers linear boundary conditions for each time step in order to circumvent the difficulties arising from the nonlinear coupling in the original boundary conditions. We prove the well-posedness of the θ-flux Neumann problems for θ > 0 and obtain a solution of the standard (zero-flux) Neumann problem as the limit for θ → 0 of solutions of the θ-flux Neumann problems. Concerning applications, the analysis developed here supports a new model for the settling of polydisperse suspensions forming compressible sediments. © 2006 Society for Industrial and Applied Mathematics.

Más información

Título según WOS: Neumann problems for quasi-linear parabolic systems modeling polydisperse suspensions
Título según SCOPUS: Neumann problems for quasi-linear parabolic systems modeling polydisperse suspensions
Título de la Revista: SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Volumen: 38
Número: 2
Editorial: SIAM PUBLICATIONS
Fecha de publicación: 2006
Página de inicio: 557
Página final: 573
Idioma: English
URL: http://epubs.siam.org/doi/abs/10.1137/050635195
DOI:

10.1137/050635195

Notas: ISI, SCOPUS - WOS