Mathematical Sciences: Problems in Nonlinear Partial Differential Equations

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This project supports graduate students working with Professor Joel Smoller on problems in geometrical partial differential equations. Particular emphasis is placed upon the study of spherically symmetric Einstein-Maxwell and Einstein- Yang-Mills equations. More generally, semilinear elliptic equations and systems with symmetry are studied from the point of view of bifurcation theory and symmetry-breaking. The associated time dependent problems are studied using topological techniques such as the connection-matrix method. The particular equations under consideration have relevance to areas of mathematical physics such as cosmology, gravitation and the formation and stability of black holes.