Peter Markowich (KAUST / Cambridge / Vienna): Mathematical Analysis of a PDE System for
Biological Network Formation
Tuesday, 03.02.2015 14:15 im Raum SRZ 105
Abstract:
Motivated by recent physics papers describing basis principles
for biological network formation, we study an elliptic-parabolic
system of partial differential equations proposed by D. Hu and
D. Cai in 2012. The model describes the pressure field by a
Darcys type equation and the dynamics of the network
conductance under pressure force effects with diffusion
representing randomness in the material structure. We prove
the existence of global weak solutions and of local mild
solutions and study their long time behavior.
It turns out that, by energy dissipation, steady states play a
central role in understanding the pattern capacity of the
system. We show that for a large diffusion coefficient, the zero
steady stateis stable. Patterns occur for small values of the
diffusion coefficient because the zero steady state is Turing
unstable in this range; for vanishing diffusion we can exhibit a
large class of dynamically stable (in the linearized sense) steady
states.
Angelegt am Wednesday, 28.01.2015 10:43 von Martin Burger
Geändert am Wednesday, 28.01.2015 10:43 von Martin Burger
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