Premium
Transport equation with boundary conditions of hysteresis type
Author(s) -
Amler T. G.,
Botkin N. D.,
Hoffmann K.H.,
Meirmanov A. M.,
Starovoitov V. N.
Publication year - 2009
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1127
Subject(s) - uniqueness , mathematics , boundary value problem , nonlinear system , bounded function , work (physics) , boundary (topology) , mathematical analysis , type (biology) , convection–diffusion equation , convection , fluid dynamics , saturation (graph theory) , inlet , mechanics , thermodynamics , physics , geology , geomorphology , paleontology , quantum mechanics , combinatorics
This paper is an advanced extension of the work reported in ( Nonlinear Anal. 2005; 63 :1467–1473). A transport equation that describes the propagation of a substance in a moving fluid or gas is considered. The equation contains the transient, convection, and diffusion terms. The problem is formulated in a bounded domain provided with an inlet and an outlet for the fluid or gas flow. The crucial point of the problem setting is a hysteresis‐type condition posed on an active part of the boundary. This condition reflects the nondecreasing accumulation with saturation of the transported substance at each point of the active boundary part. We prove the existence and uniqueness of solutions to this problem, study the regularity properties of solutions, and perform numerical simulations that clarify the behavior of the model. Comparing with the results of ( Nonlinear Anal. 2005; 63 :1467–1473), the advancement of this work consists in accounting for the motion of the fluid or gas and posing inlet and outlet boundary conditions. Copyright © 2009 John Wiley & Sons, Ltd.