
Title: Homotopy continuation methods for nonlinear PDEs and applications
Abstract: This talk will cover some recent work on homotopy continuation and bootstrapping methods to solve systems of nonlinear partial differential equations (PDEs) arising from biology and physics. This new approach, which is used to compute multiple solutions and bifurcation of nonlinear PDEs, makes use of polynomial systems (with thousands of variables) arising by discretization. Examples from hyperbolic systems, tumor growth models, and a blood clotting model will be used to demonstrate the ideas.