Thomas P. Witelski

Journal article Discrete and Continuous Dynamical Systems Series A · March 1, 2023 Featured Publication We consider the porous medium equation subject to zero-Dirichlet conditions on a variety of two-dimensional domains, namely strips, slender domains and sectors, allowing us to capture a number of different classes of behaviours. Our focus is on intermediat ... Full text Cite

Pressure-dipole solutions of the thin-film equation

Journal article European Journal of Applied Mathematics · April 1, 2019 Featured Publication We investigate self-similar sign-changing solutions to the thin-film equation, h t = -(|h| n h xxx ) x , on the semi-infinite domain x ≥ 0 with zero-pressure-type boundary conditions h = h xx = 0 impos ... Full text Cite

Instability and dynamics of volatile thin films

Journal article Physical Review Fluids · February 1, 2018 Featured Publication Volatile viscous fluids on partially wetting solid substrates can exhibit interesting interfacial instabilities and pattern formation. We study the dynamics of vapor condensation and fluid evaporation governed by a one-sided model in a low-Reynolds-number ... Full text Cite

Methods of Mathematical Modelling: Continuous Systems and Differential Equations

Book · September 18, 2015 Featured Publication This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such a ... Full text Cite

Exponential Asymptotics for Thin Film Rupture.

Journal article SIAM J. Appl. Math. · 2013 Featured Publication Full text Cite