Professor Philip Broadbridge, La Trobe University
Dr Dimetre Triadis, La Trobe University
Partial differential equations (PDEs) model an enormous variety of continuum dynamic processes, including fluid dynamics, elasticity, solute and heat diffusion, subterranean hydrology, population dynamics, electromagnetic fields and gravity. Nonlinearity (or dependence of PDE coeffcients on dependent variables) is essential to explain some familiar phenomena such as thermal ignition and wave breaking. Some helpful techniques will be applied to develop a conceptual understanding of nonlinear waves and nonlinear diffusive processes, with minimal theory of function spaces. These techniques will include the method of characteristics, asymptotic approximations, symmetry reduction and integrable models.
Part A (nonlinear waves; 11 lectures and 2 problem-solving sessions)
Part B (nonlinear diffusion; 11 lectures and 2 problem-solving sessions)
Take this quiz and look at some of the expected foundational skills in this topic
Professor Philip Broadbridge,
La Trobe University
Phil Broadbridge was educated at University of Adelaide and University of Tasmania. He has previously worked as a high school teacher and as a CSIRO research scientist. He served as a professor for 28 years at Wollongong, Delaware, AMSI/Melbourne and La Trobe. His research has mostly been on various applications of partial differential equations in physics, hydrology, heat conduction, materials science and biology. He now has honorary professor positions at Wollongong, Kyushu and La Trobe.
Dr Dimetre Triadis,
La Trobe University
Dimetre is a research fellow employed jointly at the Department of Mathematics and Statistics, La Trobe University, and the Institute of Mathematics for Industry, Kyushu University, Japan. His research is focused on exact solutions for nonlinear partial differential equations occurring in elastic contact problems, soil water infiltration, nonlinear heat conduction, and other applications.