Blow-up phenomena in semilinear elliptic partial differential equations

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This project will address important questions in semilinear elliptic partial differential equations. It will determine the existence, multiplicity, breaking of symmetry, and concentration phenomena of solutions of semilinear partial differential equations. The asymptotic behaviour of solutions in semilinear equations has enormous potential to impact on fields in which differential equations can be applied to simple mechanical systems, and built and diverse natural phenomena such as suspension bridges, galaxies and mathematical biology problems.