Some open questions concerning biological growth

TL;DR

This paper reviews simplified models of biological growth focusing on radially growing interfaces, highlighting exact solutions for linear models and discussing open questions in nonlinear cases.

Contribution

It provides a concise overview of mathematical models for biological growth, emphasizing the distinction between linear and nonlinear equations and their solvability.

Findings

Linear models are exactly solvable, providing clear insights into growth phenomenology.

Nonlinear models present open questions and complex behaviors.

The paper connects interface growth properties to biological processes.

Abstract

We briefly review the properties of radially growing interfaces and their connection to biological growth. We focus on simplified models which result from the abstraction of only considering domain growth and not the interface curvature. Linear equations can be exactly solved and the phenomenology of growth can be inferred from the explicit solutions. Nonlinear equations pose interesting open questions that are summarized herein.