In this work we address a problem governed by linear parabolic partial differential equations set in two adjoining domains, coupled by nonlinear interface conditions of Neumann type. In particular, we address the existence and uniqueness of strong solutions by applying the strong maximum principle, the Schauder fixed point theorem and the fundamental solutions of linear parabolic partial differential equations. In the first part of this work, we consider the properties of a linear parabolic partial differential equation set on a single domain with a nonlinear boundary condition. After having addressed the well-posedness and some comparison results for the problem on one domain, in the second part of this work we address the case of coupled problems on adjoining domains. In both cases, we complete the understanding of the behavior of the solution of the problems at hand by means of numerical simulations. The theoretical results obtained here are applied to study the behavior of a biological model for the transfer of chemicals through thin biological membranes. This model represents the dynamics of the concentration u of a chemical solution separated from the exterior by a semi-permeable membrane.

Analysis of parabolic problems on partitioned domains with nonlinear conditions at the interface. Application to mass transfer through semi-permeable membranes.

CALABRO', Francesco;
2006

Abstract

In this work we address a problem governed by linear parabolic partial differential equations set in two adjoining domains, coupled by nonlinear interface conditions of Neumann type. In particular, we address the existence and uniqueness of strong solutions by applying the strong maximum principle, the Schauder fixed point theorem and the fundamental solutions of linear parabolic partial differential equations. In the first part of this work, we consider the properties of a linear parabolic partial differential equation set on a single domain with a nonlinear boundary condition. After having addressed the well-posedness and some comparison results for the problem on one domain, in the second part of this work we address the case of coupled problems on adjoining domains. In both cases, we complete the understanding of the behavior of the solution of the problems at hand by means of numerical simulations. The theoretical results obtained here are applied to study the behavior of a biological model for the transfer of chemicals through thin biological membranes. This model represents the dynamics of the concentration u of a chemical solution separated from the exterior by a semi-permeable membrane.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11580/12755
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 18
social impact