Open Access
2001 Periodic solutions of a nonlinear evolution problem from heterogeneous catalysis
Dieter Bothe
Differential Integral Equations 14(6): 641-670 (2001). DOI: 10.57262/die/1356123241


We consider a class of reaction-diffusion systems with macroscopic convection and nonlinear diffusion plus a nonstandard boundary condition which results as a model for heterogeneous catalysis in a stirred multiphase chemical reactor. Since the appearance of $T$-periodic feeds is a common feature in such applications, we study the problem of existence of a $T$-periodic solution. The model under consideration admits an abstract formulation in an appropriate $L^1$-setting, which leads to an evolution problem of the type \[ u' + Au \ni f(t,u) \ \mbox{ on } \ \mathbb R_+. \] Here $A$ is an $m$-accretive operator in a Banach space $X$ and $f:\mathbb R_+ \times K \to X$ is $T$-periodic and of Carathéodory type where $K$ is a closed, bounded, convex subset of $X$. Sufficient conditions on $A$, $f$ and $K$ to assure existence of $T$-periodic mild solutions for this evolution problem are provided and applied to the class of reaction-diffusion systems mentioned above.


Download Citation

Dieter Bothe. "Periodic solutions of a nonlinear evolution problem from heterogeneous catalysis." Differential Integral Equations 14 (6) 641 - 670, 2001.


Published: 2001
First available in Project Euclid: 21 December 2012

zbMATH: 1032.34061
MathSciNet: MR1826955
Digital Object Identifier: 10.57262/die/1356123241

Primary: 34G20
Secondary: 34A60 , 35K55 , 47J35

Rights: Copyright © 2001 Khayyam Publishing, Inc.

Vol.14 • No. 6 • 2001
Back to Top