scholarly journals A codimension-two free boundary problem for the equilibrium shapes of a small three-dimensional island in an epitaxially strained solid film

2002 ◽  
pp. 1-25 ◽  
Author(s):  
L. Shanahan ◽  
Brian Spencer
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Three Dimensional ◽  
Codimension Two ◽  
Solid Film ◽  
Equilibrium Shapes

scholarly journals Hopf Bifurcation with the Spatial Average of an Activator in a Radially Symmetric Free Boundary Problem

2010 ◽  
Vol 2010 ◽  
pp. 1-18
Author(s):  
YoonMee Ham
Keyword(s):  
Hopf Bifurcation ◽  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Interface Problem ◽  
Spatial Average ◽  
Radially Symmetric Solutions ◽  
Dimensional Ball

An interface problem derived by a bistable reaction-diffusion system with the spatial average of an activator is studied on ann-dimensional ball. We analyze the existence of the radially symmetric solutions and the occurrence of Hopf bifurcation as a parameter varies in two and three-dimensional spaces.

ADVECTION-DIFFUSION MODELS FOR SOLID TUMOUR EVOLUTION IN VIVO AND RELATED FREE BOUNDARY PROBLEM

2000 ◽  
Vol 10 (03) ◽  
pp. 379-407 ◽  
Author(s):  
E. DE ANGELIS ◽  
L. PREZIOSI
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Tumour Size ◽  
Three Dimensional ◽  
Parabolic Type ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Three Dimensional Model

This paper proposes a multicell model to describe the evolution of tumour growth from the avascular stage to the vascular one through the angiogenic process. The model is able to predict the formation of necrotic regions, the control of mitosis by the presence of an inhibitory factor, the angiogenesis process with proliferation of capillaries just outside the tumour surface with penetration of capillary sprouts inside the tumour, the regression of the capillary network induced by the tumour when angiogenesis is controlled or inhibited, say as an effect of angiostatins, and finally the regression of the tumour size. The three-dimensional model is deduced both in a continuum mechanics framework and by a lattice scheme in order to put in evidence the relation between microscopic phenomena and macroscopic parameters. The evolution problem can be written as a free-boundary problem of mixed hyperbolic–parabolic type coupled with an initial-boundary value problem in a fixed domain.

Uniqueness of solution to a free boundary problem from combustion with transport

MAT Serie A ◽  
2001 ◽  
Vol 5 ◽  
pp. 37-41
Author(s):  
Claudia Lederman ◽  
Juan Luis Vázquez ◽  
Noemí Wolanski
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Uniqueness Of Solution ◽  
A Free Boundary Problem
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