About me

I am a Professor and Head of Department at Mathematics Department, Swansea University.

My research is in the Analysis of Nonlinear Partial Differential Equations (PDE). I use methods from the Calculus of Variations and Potential Theory to address fundamental properties of nonlinear elliptic equations, such as existence, qualitative properties and asymptotic decay of solutions, concentration, blow-up and singular phenomena. My recent work is focussed on Choquard and Schrödinger-Poisson type equations and other classes of nonlinear equations with nonlocal interactions. Such equations describe collective behaviour of self-interacting many-body systems at different scales, from atom and molecules to flock patterns in animal swarms and up to formation of stars and galaxies. The common mathematical feature of all these models is that, unlike in the case of classical local PDEs, nonlocal terms are present in the equations via Coulombian type interactions or via a fractional Laplacian term, or both.

My earlier research interests were in the area of topological and variational methods of Nonlinear Analysis, in particular in Critical Points Theory, infinite dimensional Morse Theory and applications to nonlinear elliptic equations and nonlinear problems associated with non-local integral operators.

I am always interested to hear from candidates for a PhD or a postdoctoral position in the area of Nonlinear PDEs.

My undergraduate teaching portfolio consists of a broad variety of courses in Analysis and Differential Equations.

In the recent years I held several key administrative roles within the department. I am also involved in several external editorial and research advisory roles.

Department of Mathematics
Swansea University
Swansea SA1 8EN
Wales, UK

+44 (0)1792 602763
Office: 322 CoFo

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