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Research interests

Current research interests are in Asymptotic Analysis and Perturbation Methods, with focus on Industrial and Applied Mathematical Modelling. Main areas include:

(1) Complex fluids with memory - these are fluids that behave as both liquids and solids. Applications in polymer, food, petroleum and minerals industries, inkjet printing, nanotechnology, smart materials and intelligent gels.

(2) High order nonlinear evolutionary PDEs - Fourth, sixth and tenth order Cahn-Hilliard and thin film type equations (semi-linear and degenerate quasi-linear PDEs).

(3) Free boundary problems

(a) Engineering applications: heat and mass transfer, semiconductor fabrication (silicon oxidation and device isolation techniques), concrete carbonation.

(b) Finance: Pricing of American style options/derivatives. Fractal identification in pricing data.

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