Journal article
A nonlinear transport problem of hyperbolic-elliptic type
Bulletin of the Brazilian Mathematical Society, New Series, Vol.47(1), pp.373-379
03/2016
DOI: 10.1007/s00574-016-0145-y
Abstract
A nonlinear transport problem of hyperbolic-elliptic type is studied. Using estimates of potentials over varying domains and the method of characteristics, the initial value problem for Hölder continuous data can be treated as an abstract evolution equation via Picard-Lindelöf theorem. In addition, a global existence result is proved. Modifications of these techniques yield shock front solutionswith smooth interfaces and an extension to the case of only bounded initial values. Moreover, long time behavior of solutions and the relation to diffeomorphisms with prescribed Jacobian determinants are analyzed.
Details
- Title: Subtitle
- A nonlinear transport problem of hyperbolic-elliptic type
- Creators
- Hans-Peter Gittel - Department of Mathematics University of Leipzig Augustusplatz 10 04109 Leipzig GermanyMatthias Günther - Department of Mathematics University of Leipzig Augustusplatz 10 04109 Leipzig GermanyGerhard Ströhmer - Department of Mathematics University of Iowa Iowa City IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Bulletin of the Brazilian Mathematical Society, New Series, Vol.47(1), pp.373-379
- Publisher
- Springer Berlin Heidelberg; Berlin/Heidelberg
- DOI
- 10.1007/s00574-016-0145-y
- ISSN
- 1678-7544
- eISSN
- 1678-7714
- Language
- English
- Date published
- 03/2016
- Academic Unit
- Mathematics
- Record Identifier
- 9983986089402771
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