Advection-driven support shrinking in a chemotaxis model with degenerate mobility

J.L. Fischer, SIAM Journal on Mathematical Analysis 45 (2013) 1585–1615.

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Abstract
We derive sufficient conditions for advection-driven backward motion of the free boundary in a chemotaxis model with degenerate mobility. In this model, a porous-medium-type diffusive term and an advection term are in competition. The former induces forward motion, the latter may induce backward motion of the free boundary depending on the direction of advection. We deduce conditions on the growth of the initial data at the free boundary which ensure that at least initially the advection term is dominant. This implies local backward motion of the free boundary provided the advection is (locally) directed appropriately. Our result is based on a new class of moving test functions and Stampacchia's lemma. As a by-product of our estimates, we obtain quantitative bounds on the spreading of the support of solutions for the chemotaxis model and provide a proof for the finite speed of the support propagation property of solutions.
Publishing Year
Date Published
2013-01-01
Journal Title
SIAM Journal on Mathematical Analysis
Volume
45
Issue
3
Page
1585 - 1615
IST-REx-ID

Cite this

Fischer JL. Advection-driven support shrinking in a chemotaxis model with degenerate mobility. SIAM Journal on Mathematical Analysis. 2013;45(3):1585-1615. doi:10.1137/120874291
Fischer, J. L. (2013). Advection-driven support shrinking in a chemotaxis model with degenerate mobility. SIAM Journal on Mathematical Analysis, 45(3), 1585–1615. https://doi.org/10.1137/120874291
Fischer, Julian L. “Advection-Driven Support Shrinking in a Chemotaxis Model with Degenerate Mobility.” SIAM Journal on Mathematical Analysis 45, no. 3 (2013): 1585–1615. https://doi.org/10.1137/120874291.
J. L. Fischer, “Advection-driven support shrinking in a chemotaxis model with degenerate mobility,” SIAM Journal on Mathematical Analysis, vol. 45, no. 3, pp. 1585–1615, 2013.
Fischer JL. 2013. Advection-driven support shrinking in a chemotaxis model with degenerate mobility. SIAM Journal on Mathematical Analysis. 45(3), 1585–1615.
Fischer, Julian L. “Advection-Driven Support Shrinking in a Chemotaxis Model with Degenerate Mobility.” SIAM Journal on Mathematical Analysis, vol. 45, no. 3, Society for Industrial and Applied Mathematics , 2013, pp. 1585–615, doi:10.1137/120874291.

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