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Full-Text Articles in Physical Sciences and Mathematics
A Simplified Model For Growth Factor Induced Healing Of Wounds, F. J. Vermolen, E. Van Baaren, J. A. Adam
A Simplified Model For Growth Factor Induced Healing Of Wounds, F. J. Vermolen, E. Van Baaren, J. A. Adam
Mathematics & Statistics Faculty Publications
A mathematical model is developed for the rate of healing of a circular or elliptic wound. In this paper the regeneration, decay and transport of a generic 'growth factor', which induces the healing of the wound, is taken into account. Further, an equation of motion is derived for radial healing of a circular wound. The expressions for the equation of motion and the distribution of the growth factor are related in such a way that no healing occurs if the growth factor concentration at the wound edge is below a threshold value. In this paper we investigate the influence of …
On The Existence Of Strong Solutions To Autonomous Differential Equations With Minimal Regularity, Charlie H. Cooke
On The Existence Of Strong Solutions To Autonomous Differential Equations With Minimal Regularity, Charlie H. Cooke
Mathematics & Statistics Faculty Publications
For proving the existence and uniqueness of strong solutions to
dY/dt = F(Y), Y(0) = C,
the most quoted condition seen in elementary differential equations texts is that F(Y) and its first derivative be continuous. One wonders about the existence of a minimal regularity condition which allows unique strong solutions. In this note, a bizarre example is seen where F(Y) is not differentiable at an equilibrium solution; yet unique non-global strong solutions exist at each point, whereas global non-unique weak solutions are allowed. A characterizing theorem is obtained.
A System Equivalence Related To Dulac's Extension Of Bendixson's Negative Theorem For Planar Dynamical Systems, Charlie H. Cooke
A System Equivalence Related To Dulac's Extension Of Bendixson's Negative Theorem For Planar Dynamical Systems, Charlie H. Cooke
Mathematics & Statistics Faculty Publications
Bendixson's Theorem [H. Ricardo, A Modem Introduction to Differential Equations, Houghton-Mifflin, New York, Boston, 2003] is useful in proving the non-existence of periodic orbits for planar systems
dx/dt = F(x, y), dy/dt = G (x, y)
in a simply connected domain D, where F, G are continuously differentiable. From the work of Dulac [M. Kot, Elements of Mathematical Ecology, 2nd printing, University Press, Cambridge, 2003] one suspects that system (1) has periodic solutions if and only if the more general system
dx/d tau = B(x, y)F(x, y), dy/d tau = B(x, y)G(x, y)
does, which makes the subcase (1) more …