Journal article
Remarks on a nonlinear transport problem
Journal of Differential Equations, Vol.256(3), pp.957-988
02/01/2014
DOI: 10.1016/j.jde.2013.10.002
Abstract
A nonlinear transport problem of hyperbolic–elliptic type is studied. Estimates of potentials over varying domains and the method of characteristics enable one to treat the initial value problem for Hölder continuous data as an abstract evolution equation via Picard–Lindelöf theorem. In addition, existence for all times is proved. Similar techniques yield the existence of shock front solutions with smooth interfaces at least for a small time interval. By a priori estimates of approximating solutions, the results extend to the case of only bounded initial values. A modification of the system applies to the construction of a diffeomorphism with prescribed Jacobian determinant.
Details
- Title: Subtitle
- Remarks on a nonlinear transport problem
- Creators
- Hans-Peter Gittel - Mathematisches Institut, Universität Leipzig, Augustusplatz 10, 04109 Leipzig, GermanyMatthias Günther - Mathematisches Institut, Universität Leipzig, Augustusplatz 10, 04109 Leipzig, GermanyGerhard Ströhmer - Department of Mathematics, University of Iowa, Iowa City, IA, 52242, USA
- Resource Type
- Journal article
- Publication Details
- Journal of Differential Equations, Vol.256(3), pp.957-988
- DOI
- 10.1016/j.jde.2013.10.002
- ISSN
- 0022-0396
- eISSN
- 1090-2732
- Publisher
- Elsevier Inc
- Language
- English
- Date published
- 02/01/2014
- Academic Unit
- Mathematics
- Record Identifier
- 9983986096802771
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