Mathematical Sciences: Spatial and Temporal Nonlinear Integral and Differential Equations

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This project will attempt to the analysis of neural nets to incorporate synaptic delay and also use recent results to analyze large amplitude behavior of simple neural nets. The behavior large numbers of coupled nonlinear oscillators will be analyzed as a model for synchrony. Models of aggregation and branching will be studied both numerically and analytically. Work on models for corticotopic maps will continue. Most of the problems involve nonlinear integro-differential equations and how they apply to biological phenomena. The PI's will also continue their studies of a nonlinear fourth order boundary value problem which models fluid flow past a stretching sheet. In addition studies of second order semilinear elliptic equations will be continued. In particular the question of uniqueness of solutions with prescribed numbers of zeros will be addressed. Finally, finite time blow-up in Schrodinger's equation will be investigated.