The Riemann problem for a forward–backward parabolic equation

The Riemann problem for a forward–backward parabolic equation of interest in physical and biological models is studied. A complete classification of suitably defined entropy solutions is provided. Thereafter, the existence and uniqueness of a solution is proven, and its type is identified.

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Bibliographic Details
Published in:Physica. D 2010-03, Vol.239 (6), p.291-311
Main Authors: Gilding, Brian H., Tesei, Alberto
Format: Article
Language:English
Subjects:
Classification
Discontinuity
Entropy weak solution
Exact sciences and technology
Existence
Forward–backward parabolic equation
Ill posed
Phase transition
Physics
Riemann problem
Uniqueness
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Description
Summary:The Riemann problem for a forward–backward parabolic equation of interest in physical and biological models is studied. A complete classification of suitably defined entropy solutions is provided. Thereafter, the existence and uniqueness of a solution is proven, and its type is identified.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2009.10.006