Using mathematical models to simulate dynamic biological processes has a long history.
Over the past couple of decades or so, quantitative approaches have also made their way …

In the nearly seven decades since the publication of Alan Turing's work on morphogenesis,
enormous progress has been made in understanding both the mathematical and biological …

In this article we consider finite element methods for approximating the solution of partial
differential equations on surfaces. We focus on surface finite elements on triangulated …

Despite major scientific, medical and technological advances over the last few decades, a
cure for cancer remains elusive. The disease initiation is complex, and including initiation …

This review will outline a number of illustrative mathematical models describing the growth
of avascular tumors. The aim of the review is to provide a relatively comprehensive list of …

Tumour growth is a multifactorial process, which has stimulated in recent decades the
development of numerous models trying to figure out the mechanisms controlling solid …

In this paper, we present and investigate a model for solid tumor growth that incorporates
features of the tumor microenvironment. Using analysis and nonlinear numerical …

Recent examples of biological pattern formation where a pattern changes qualitatively as
the underlying domain grows have given rise to renewed interest in the reaction-diffusion …

In this article we propose models and a numerical method for pattern formation on evolving
curved surfaces. We formulate reaction-diffusion equations on evolving surfaces using the …

This paper deals with the effects of partial differential equations on the development of
spatiotemporal patterns in reaction–diffusion systems. These systems describe how the …