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On scalar conservation laws with point source and discontinuous flux function

Diehl, Stefan LU (1995) In SIAM Journal on Mathematical Analysis 26(6). p.1425-1451
Abstract
The conservation law studied is partial derivative u(x,t)/partial derivative t + partial derivative/partial derivative x (F(u(x,t),x)) = s(t)delta(x), where u is a concentration, s is a source, delta is the Dirac measure, and is the flux function. The special feature of this problem is the discontinuity that appears along the t-axis and the curves of discontinuity that go into and emanate from it. Necessary conditions for the existence of La piecewise smooth solution are given. Under some regularity assumptions sufficient conditions are given enabling construction of piecewise smooth solutions by the method of characteristics. The selection of a unique solution is made by a coupling condition at x = 0, which is a generalization of the... (More)
The conservation law studied is partial derivative u(x,t)/partial derivative t + partial derivative/partial derivative x (F(u(x,t),x)) = s(t)delta(x), where u is a concentration, s is a source, delta is the Dirac measure, and is the flux function. The special feature of this problem is the discontinuity that appears along the t-axis and the curves of discontinuity that go into and emanate from it. Necessary conditions for the existence of La piecewise smooth solution are given. Under some regularity assumptions sufficient conditions are given enabling construction of piecewise smooth solutions by the method of characteristics. The selection of a unique solution is made by a coupling condition at x = 0, which is a generalization of the classical entropy condition and is justified by studying a discretized version of the problem by Godunov's method.



The motivation for studying this problem is the fact that it arises in the modelling of continuous sedimentation of solid particles in a liquid. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
POINT SOURCE, DISCONTINUOUS FLUX, CONSERVATION LAWS, CONVEXITY
in
SIAM Journal on Mathematical Analysis
volume
26
issue
6
pages
1425 - 1451
publisher
Society for Industrial and Applied Mathematics
ISSN
0036-1410
DOI
10.1137/S0036141093242533
language
English
LU publication?
yes
id
4b6be729-22f4-4013-a9ec-1db5a9e9c53b (old id 779704)
date added to LUP
2016-04-04 09:04:25
date last changed
2018-11-21 20:50:34
@article{4b6be729-22f4-4013-a9ec-1db5a9e9c53b,
  abstract     = {{The conservation law studied is partial derivative u(x,t)/partial derivative t + partial derivative/partial derivative x (F(u(x,t),x)) = s(t)delta(x), where u is a concentration, s is a source, delta is the Dirac measure, and is the flux function. The special feature of this problem is the discontinuity that appears along the t-axis and the curves of discontinuity that go into and emanate from it. Necessary conditions for the existence of La piecewise smooth solution are given. Under some regularity assumptions sufficient conditions are given enabling construction of piecewise smooth solutions by the method of characteristics. The selection of a unique solution is made by a coupling condition at x = 0, which is a generalization of the classical entropy condition and is justified by studying a discretized version of the problem by Godunov's method.<br/><br>
<br/><br>
The motivation for studying this problem is the fact that it arises in the modelling of continuous sedimentation of solid particles in a liquid.}},
  author       = {{Diehl, Stefan}},
  issn         = {{0036-1410}},
  keywords     = {{POINT SOURCE; DISCONTINUOUS FLUX; CONSERVATION LAWS; CONVEXITY}},
  language     = {{eng}},
  number       = {{6}},
  pages        = {{1425--1451}},
  publisher    = {{Society for Industrial and Applied Mathematics}},
  series       = {{SIAM Journal on Mathematical Analysis}},
  title        = {{On scalar conservation laws with point source and discontinuous flux function}},
  url          = {{http://dx.doi.org/10.1137/S0036141093242533}},
  doi          = {{10.1137/S0036141093242533}},
  volume       = {{26}},
  year         = {{1995}},
}