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Epidermal wound healing is a complex process that repairs injured tissue. The complexity
of this process increases when bacteria are present in a wound; the bacteria interaction
determines whether infection sets in. Because of underlying physiological problems
infected wounds do not follow the normal healing pattern. In this paper we present a
mathematical model of the healing of both infected and uninfected wounds. At the core of
our model is an...
We discuss theoretical and experimental approaches to three distinct
developmental systems that illustrate how theory can influence experimental work
and vice-versa. The chosen systems – Drosophila melanogaster,
bacterial pattern formation, and pigmentation patterns – illustrate the
fundamental physical processes of signaling, growth and cell division, and cell
movement involved in pattern formation and development. These systems exemplify
the current state of theoretical and experimental understanding...
We present the Rothe method for the McKendrick-von Foerster equation with initial and boundary conditions. This method is well known as an abstract Euler scheme in extensive literature, e.g. K. Rektorys, The Method of Discretization in Time and Partial Differential Equations, Reidel, Dordrecht, 1982. Various Banach spaces are exploited, the most popular being the space of bounded and continuous functions. We prove the boundedness of approximate solutions and stability of the Rothe method in and...
In this article a variational reduction method, how to handle the case of heterogenous
domains for the Transport equation, is presented. This method allows to get rid of the
restrictions on the size of time steps due to the thin parts of the domain. In the thin
part of the domain, only a differential problem, with respect to the space variable, is to
be approximated numerically. Numerical results are presented with a simple example. The
variational...
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