LONG-TIME BEHAVIOR OF SOLUTIONS OF A NONLINEAR DIFFUSION MODEL WITH TRANSMISSION BOUNDARY CONDITIONS

TitleLONG-TIME BEHAVIOR OF SOLUTIONS OF A NONLINEAR DIFFUSION MODEL WITH TRANSMISSION BOUNDARY CONDITIONS
Publication TypeJournal Article
Year of Publication2009
AuthorsANDERSON JEFFREYR
JournalDynamic Systems and Applications
Volume18
Start Page111
Pagination10
Date Published2009
ISSN1056-2176
AMS Subject Classification35B05, 35K65
Abstract

In order to accurately simulate the transport of growth factor from tumor site into a nearby capillary wall, a recently introduced model of tumor-induced capillary growth incorporates a new form of transmission boundary flux. Growth factor emitted from the tumor may be viewed as a diffusible chemical moving through intersticial space, which is represented as a porous medium. Transmission between the capillary wall and intersticial space gives rise to a type of continuous delay/memory condition at the boundary. Herein, we establish results on global solvability and blow up in finite time for a general nonlinear diffusion model, including such transmission boundary conditions. Although the model appears more closely aligned with models involving nonlinear flux conditions at the boundary, these results bear notable similarities to those with Dirichlet boundary conditions.

PDFhttps://acadsol.eu/dsa/articles/18/09-DSA-CY-9-Anderson.pdf
Refereed DesignationRefereed