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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166314We 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.20 pages, packages used: amsmath, amssymb, amsthm, mathrsfs, bbm, nicefracAnalysis of PDEs34D23, 35K45, 35K50, 35K55, 35K57, 92C37, 92C45Contraction in $L^1$ and large time behavior for a system arising in chemical reactions and molecular motorstext