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A Nonlocal Conservation Law from a Model of Granular Flow

Summary: 1
A Nonlocal Conservation Law from a Model
of Granular Flow
Debora Amadori
Department of Pure & Applied Mathematics, University of L'Aquila
L'Aquila, I-67010 Italy.
E-mail: amadori@univaq.it
Wen Shen
Department of Mathematics, Penn State University, USA
University Park, PA 16802 USA.
E-mail: shen w@math.psu.edu
In this paper we study the well-posedness for a scalar conser-
vation law in which the flux term is non-local in space.
This equation represents a reduced model for slow erosion in
granular flow ([1, 6]) and describes roughly the evolution of a
profile of stationary matter, under the effect of a thin moving
layer of granular matter on the top of it.
We show that the present equation admits weak solutions ex-
isting globally in time and prove their stability w.r.t the initial


Source: Amadori, Debora - Dipartimento di Matematica Pura e Applicata, UniversitÓ dell'Aquila


Collections: Mathematics