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Personal profile

Research interests

I research into differential equations, mostly PDEs, and their applications. Much of my work concerns diffusion-type equations and I am particularly interested in blow-up, as can model explosions or ignition, free-boundary problems, such as phase-change models, and models with non-local terms I am also interested in mathematical modelling of industrial, societal, and other problems, from bread baking and welding to homelessness and housing allocation. Many of these research areas originate through interaction with the Industrial Mathematics KTN and particularly the Study Groups with Industry.


I received my D.Phil. in mathematics at Oxford in 1979, then held post-doctoral fellowships, in both Oxford and Wellington. My work in this period concerned: Free-boundary problems, including both freezing/melting and the famous Hele-Shaw problem. Ignition, using both ODE and parabolic-equation models. A high-order parabolic model for thin-film flow. I was appointed lecturer at Heriot-Watt in 1982, reader in 1987, professor in 1996, and elected fellow of the Royal Society of Edinburgh in 1990. Here I have continued my earlier research, proving key results on blow-up for parabolic equations, and on free-boundary motion. Largely through participation in Study Groups with Industry, I have also studied diverse practical problems: Industrial, including calorimetry, bread crusts and green roofs (collaborating companies have been small, SMEs, and large, such as RHM). Scientific, such as fire spread. Social, such as homelessness levels.

Fingerprint Fingerprint is based on mining the text of the person's scientific documents to create an index of weighted terms, which defines the key subjects of each individual researcher.

Welding Mathematics
Free Boundary Mathematics
Blow-up Mathematics
Friction Mathematics
Nonlocal Problems Mathematics
melting Physics & Astronomy
Heating Mathematics
Quenching Mathematics

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Research Output 1983 2016

A mathematical model of serious and minor criminal activity

Lacey, A. A. & Tsardakas, M., Jun 2016, In : European Journal of Applied Mathematics. 27, 3, p. 403-421 19 p.

Research output: Contribution to journalArticle

Open Access
mathematical method
statistical analysis

Determining the twist in an optical fiber

Lacey, A. A., Rakesh & Tang, J., 24 Feb 2016, In : Inverse Problems. 32, 3, 28 p., 035008.

Research output: Contribution to journalArticle

Open Access
optical fibers
hyperbolic systems

On the quenching of a nonlocal parabolic problem arising in electrostatic MEMS control

Lacey, A. A., Kavallaris, N. & Nikolopoulos, C., Jun 2016, In : Nonlinear Analysis: Theory, Methods and Applications. 138, p. 189–206 18 p.

Research output: Contribution to journalArticle

Open Access
Nonlocal Problems
Parabolic Problems
Micro-electro-mechanical Systems

A Mathematical Model for Flash Sintering

Hewitt, I. J., Lacey, A. A. & Todd, R. I., 2 Oct 2015, In : Mathematical Modelling of Natural Phenomena. 10, 6, p. 77-89 13 p.

Research output: Contribution to journalArticle

Open Access
Mathematical models
Joule heating

Mathematical modelling of Tyndall star initiation

Lacey, A. A., Hennessy, M., Harvey, P. & Katz, R., Oct 2015, In : European Journal of Applied Mathematics. 26, 5, p. 615-645 31 p.

Research output: Contribution to journalArticle

Open Access
free boundaries
liquid-solid interfaces