On unified theory for scalar conservation laws with fluxes and sources discontinuous with respect to the unknown
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10367300" target="_blank" >RIV/00216208:11320/17:10367300 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jde.2016.09.020" target="_blank" >http://dx.doi.org/10.1016/j.jde.2016.09.020</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jde.2016.09.020" target="_blank" >10.1016/j.jde.2016.09.020</a>
Alternative languages
Result language
angličtina
Original language name
On unified theory for scalar conservation laws with fluxes and sources discontinuous with respect to the unknown
Original language description
We deal with the Cauchy problem for multi-dimensional scalar conservation laws, where the fluxes and the source terms can be discontinuous functions of the unknown. The main novelty of the paper is the introduction of a kinetic formulation for the considered problem. To handle the discontinuities we work in the framework of re-parametrization of the flux and the source functions, which was previously used for Kruikov entropy solutions. Within this approach we obtain a fairly complete picture: existence of entropy measure valued solutions, entropy weak solutions and their equivalence to the kinetic solution. The results of existence and uniqueness follow under the assumption of Holder continuity at zero of the flux. The source term, what is another novelty for the studies on problems with discontinuous flux, is only assumed to be one-side Lipschitz, not necessarily monotone function.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/LL1202" target="_blank" >LL1202: Implicitly constituted material models: from theory through model reduction to efficient numerical methods</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Differential Equations
ISSN
0022-0396
e-ISSN
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Volume of the periodical
262
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
52
Pages from-to
313-364
UT code for WoS article
000388551100009
EID of the result in the Scopus database
2-s2.0-84995527043