Differential and Integral Equations

Periodic solutions of a nonlinear evolution problem from heterogeneous catalysis

Dieter Bothe

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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.

Article information

Differential Integral Equations, Volume 14, Number 6 (2001), 641-670.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34G20: Nonlinear equations [See also 47Hxx, 47Jxx]
Secondary: 34A60: Differential inclusions [See also 49J21, 49K21] 35K55: Nonlinear parabolic equations 47J35: Nonlinear evolution equations [See also 34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx, 37Lxx, 47H20, 58D25]


Bothe, Dieter. Periodic solutions of a nonlinear evolution problem from heterogeneous catalysis. Differential Integral Equations 14 (2001), no. 6, 641--670. https://projecteuclid.org/euclid.die/1356123241

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