This second part is devoted to a series of three applications of the method of intrinsic scaling to relevant models arising from flows in porous media, chemotaxis and phase transitions.
We start with the flow of two immiscible fluids through a porous medium, proving the Hölder continuity of the saturations, which satisfy a PDE with a two-sided degeneracy. The same type of structure arises in a model for the chemotactic movement of cells under a volume-filling effect and the extension to this case, which basically consists in dealing appropriately with an extra lower order term, is also included.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(2008). Immiscible Fluids and Chemotaxis. In: The Method of Intrinsic Scaling. Lecture Notes in Mathematics, vol 1930. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75932-4_5
Download citation
DOI: https://doi.org/10.1007/978-3-540-75932-4_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75931-7
Online ISBN: 978-3-540-75932-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)