Contraction in $L^1$ and large time behavior for a system arising in chemical reactions and molecular motors

Details Contraction in $L^1$ and large time behavior for a system arising in chemical reactions and molecular motors Contraction in $L^1$ and large time behavior for a system arising in chemical reactions and molecular motors

2008-08-02

arxiv.org/abs/0808.0250v1

Mathematics

Analysis of PDEs

20 pages, packages used: amsmath, amssymb, amsthm, mathrsfs, bbm, nicefrac

Scientific paper

We prove a contraction in $L^1$ property for the solutions of a nonlinear reaction--diffusion system whose special cases include intercellular transport as well as reversible chemical reactions. Assuming the existence of stationary solutions we show that the solutions stabilize as $t$ tends to infinity. Moreover, in the special case of linear reaction terms, we prove the existence and the uniqueness (up to a multiplicative constant) of the stationary solution.

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