A transport model with adsorption hysteresis
type: Item
instance of: scholarly article
title: A transport model with adsorption hysteresis
zbMATH Open document ID: 1004.35033
author: Małgorzata Peszyńska
author: Ralph E. Showalter
published in: Differential and Integral Equations
publication date: 2000-05-29T00:00:00Z
review text: The paper deals with an initial-boundary value problem for the transport equation \((u+v)_t + u_x = 0\), \(v = {\mathcal M}u\), \(u(0,t) = \varphi (t)\), \(u(x,0) = v(x,0) = 0\), \(t \in [0,T]\), \(x \in [0,L]\), where \(\mathcal M\) is a hysteresis operator, more specifically the play operator or its combinations (the so-called Prandtl-Ishlinskij operator). Considering alternatively \(x\) and \(t\) as the `time' variable and rewriting the problem as an abstract evolution equation of the form \(U' + AU \ni f\) in \(L^2 \times L^2\) with an \(m\)-accretive operator \(A\), the authors obtain two different existence, uniqueness and regularity results. In particular, as it is often the case in hyperbolic PDEs with convex hysteresis, shocks do not occur.
Mathematics Subject Classification ID: 35F20
Mathematics Subject Classification ID: 47H06
Mathematics Subject Classification ID: 47J35
zbMATH DE Number: 1453635
zbMATH Keywords: initial-boundary value problem
zbMATH Keywords: Prandtl-Ishlinskij operator
zbMATH Keywords: abstract evolution equation
zbMATH Keywords: \(m\)-accretive operator
zbMATH Keywords: hyperbolic PDEs with convex hysteresis
reviewed by: Pavel Krejč{í }
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1453635