Publication database of NCMM , project MORE and MathMAC center.
Dear guest, welcome to this publication database. As an anonymous user, you will probably not have edit rights. Also, the collapse status of the topic tree will not be persistent. If you like to have these and other options enabled, you might ask Jaroslav Hron for a login account.
This site is powered by Aigaion - A PHP/Web based management system for shared and annotated bibliographies. For more information visit https://github.com/aigaion.
 [BibTeX] [RIS] [Request]
On unified theory for scalar conservation laws with fluxes and sources being discontinuous with respect to the unknown
Type of publication: Article
Citation:
Publication status: Published
Journal: Journal of Differential Equations
Volume: 262
Number: 1
Year: 2017
Pages: 313--364
DOI: 10.1016/j.jde.2016.09.020
Abstract: 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 Kružkov 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 Hölder 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.
Preprint project: MORE
Preprint year: 2016
Preprint number: 15
Preprint ID: MORE/2016/15
Keywords:
Authors Bulíček, Miroslav
Gwiazda, Piotr
Świerczewska-Gwiazda, Agnieszka
Added by: [MB]
Total mark: 0
Attachments
  • discont_kinetic_v2_final.pdf
Notes
    Topics