Organizers:
Fanze Kong (University of Washington), Michael Jeffrey Ward and University of British Columbia
Description:
Partial Differential Equations (PDEs) serve as a fundamental framework to describe the collective behavior and pattern formation arising in biology and ecology. Over the last several decades, there have been numerous studies devoted to analyzing pattern formation in the nonlinear regime for classical two-component reaction-diffusion (R-D) systems including Gierer-Meinhardt models, Gray-Scott models, etc. However, to analyze some specific biological and ecological processes, one must often extend this classical framework to analyze more complex PDE systems such as R-D systems with advective effects, three-component R-D systems, bulk-cell R-D systems, R-D systems on growing domains or with free boundaries, and first passage problems associated with PDEs. This minisymposium brings together scholars who seek to explore the cutting-edge challenges in the study of these complex PDE models via dynamical system approaches, PDE theories and scientific computing methods. Highlighted topics include mean first passage time problems in transport equations, localized pattern formation in three-component R-D models or growing domains, synchronization in Kuramoto-inspired bulk-cell models with spatial diffusion, and free boundary problems arising from epidemics, among others. The aim of our minisymposium is to provide a platform for an exchange of ideas and open problems at the forefront of various aspects of PDE modeling in math biology.
Jack Hughes
University of British Columbia" Pulses, Waves, and Mesas in Mass Conserved Reaction-Diffusion Media: From Theory to Actin Polymerization"
Thomas Hillen
University of Alberta"Mean First Passage Times for Transport Equations"
Chunyi Gai
The University of Northern British Columbia"An Asymptotic Analysis of Spike Self-Replication and Spike Nucleation of Reaction-Diffusion Patterns on Growing 1-D Domains"
Alan Lindsay
University of Notre Dame"Asymptotic and numerical methods for cellular signaling and directional sensing"
