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The Effect of Bacteria on Epidermal Wound Healing

E. Agyingi, S. Maggelakis, D. Ross (2010)

Mathematical Modelling of Natural Phenomena

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...

The Intersection of Theory and Application in Elucidating Pattern Formation in Developmental Biology

H. G. Othmer, K. Painter, D. Umulis, C. Xue (2009)

Mathematical Modelling of Natural Phenomena

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...

The Role of Cell-Cell Adhesion in the Formation of Multicellular Sprouts

A. Szabó, A. Czirók (2010)

Mathematical Modelling of Natural Phenomena

Collective cell motility and its guidance via cell-cell contacts is instrumental in several morphogenetic and pathological processes such as vasculogenesis or tumor growth. Multicellular sprout elongation, one of the simplest cases of collective motility, depends on a continuous supply of cells streaming along the sprout towards its tip. The phenomenon is often explained as leader cells pulling the rest of the sprout forward via cell-cell adhesion. Building on an empirically demonstrated analogy...

The solutions of the quasilinear Keller-Segel system with the volume filling effect do not blow up whenever the Lyapunov functional is bounded from below

Tomasz Cieślak (2006)

Banach Center Publications

In [2] we proved two kinds of mechanisms of preventing the blow up in a quasilinear non-uniformly parabolic Keller-Segel systems. One of them was a priori boundedness from below of the Lyapunov functional. In fact, we were able to present a condition under which the Lyapunov functional is bounded from below and a solution exists globally. In the present paper we prove that whenever the Lyapunov functional is bounded from below the solution exists globally.

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