Contraction in \(L^{1}\) for a system arising in chemical reactions and molecular motors. (English) Zbl 1171.35408

Chipot, Michel; Hilhorst, Danielle; Kinderlehrer, David; Olech, Michał

Differ. Equ. Appl. 1, No. 1, 139-151 (2009).

The authors study two specific reaction-diffusion system in which one describes a reversible reaction and other one a molecular motor. The main contribution is to establish a contraction in \(L^1\) property for the solutions of these two specific reaction-diffusion system. The existence and uniqueness of the stationary solution of the linear molecular motor problem up to a multiplicative constant are obtained.

Reviewer: Cheng He (Beijing)

MSC:

35K57	Reaction-diffusion equations
35K50	Systems of parabolic equations, boundary value problems (MSC2000)
35A05	General existence and uniqueness theorems (PDE) (MSC2000)

Keywords:

molecular motor; transport; parabolic system; contraction property