Nonlinear coupled system in thin domains with corrugated boundaries for metabolic processes

Author(s)

Cardone, Giuseppe ; Faella, Luisa ; Nakasato, Jean Carlos ; Perugia, Carmen

• Document type: Journal article
• Source: Annali di Matematica Pura ed Applicata; v. 203, n. 5, p. 36-pg., 2024-03-29.

Abstract

In this paper, we study the asymptotic behaviour of solutions of a coupled system of partial differential equations in a thin domain with oscillating boundary and varying order of thickness. In such a thin domain, our model describes the solute concentration of two different biochemical species (metabolites). The coupling between the concentrations of the metabolites is realized through reaction terms even nonlinear, appearing on the oscillating upper wall. Moreover nonlinear reaction terms appear also in the thin domain. The reaction catalyzed by the upper wall is simulated by a Robin-type boundary condition depending on a small parameter epsilon. Hence, taking into account that alpha >1 and beta >0, we analyze the coupled system by comparing the magnitude of the reaction coefficient epsilon(beta) on the upper boundary with the compression order of our thin domain, which can be epsilon or epsilon(alpha), depending on the sub-regions with different order of thickness. Comparing the exponents 1, alpha and beta, we obtain different cases for the limit problem which could appear coupled or uncoupled and allow us to identify the effects of the geometry and the physical process on the problem. Moreover it arises a critical value, i.e.beta=alpha-2, leading the reaction effects entering in the diffusion matrix. (AU)

• FAPESP's process: 23/03847-6 - Asymptotic analysis of differential equations in singularly perturbed domains
• Grantee: Jean Carlos Nakasato
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• FAPESP's process: 22/08112-1 - Boundary perturbation problems on partial differential equations
• Grantee: Jean Carlos Nakasato
• Support Opportunities: Scholarships in Brazil - Post-Doctoral