Title :
On spatially uniform behavior in reaction-diffusion systems
Author_Institution :
Dept. of Electr. Eng. & Comput. Sci., Univ. of California, Berkeley, CA, USA
fDate :
June 30 2010-July 2 2010
Abstract :
We present a condition which guarantees spatial uniformity for the asymptotic behavior of the solutions of a reaction-diffusion PDE with Neumann boundary conditions. This condition makes use of the Jacobian matrix of the reaction terms and the second Neumann eigenvalue of the Laplacian operator on the given spatial domain, and replaces the global Lipschitz assumptions commonly used in the literature with a less restrictive Lyapunov inequality. We then present numerical procedures for the verification of this Lyapunov inequality and illustrate them on models of several biochemical reaction networks.
Keywords :
partial differential equations; reaction-diffusion systems; Jacobian matrix; Laplacian operator; Lyapunov inequality; Neumann boundary conditions; Neumann eigenvalue; asymptotic behavior; biochemical reaction networks; global Lipschitz assumptions; partial differential equations; reaction-diffusion systems; Biological cells; Biological system modeling; Boundary conditions; Control systems; Eigenvalues and eigenfunctions; Jacobian matrices; Laplace equations; Linear matrix inequalities; Stability; Testing;
Conference_Titel :
American Control Conference (ACC), 2010
Conference_Location :
Baltimore, MD
Print_ISBN :
978-1-4244-7426-4
DOI :
10.1109/ACC.2010.5530549
