Paul Feehan
Nonlinear Evolutionary Equations
This course is intended for students in who are currently pursuing or would like to pursue research in geometric analysis (especially geometric flows, such as Ricci flow, mean curvature flow, etc.) or applied mathematics/partial differential equations (Navier—Stokes, nonlinear wave equations, reaction-diffusion equations, etc.).
The course is intended to complement existing graduate courses in geometric analysis that focus specifically on Ricci or mean curvature flows and courses in analysis or applied mathematics that focus on nonlinear hyperbolic or parabolic partial differential equations and qualitative properties of their solutions (such as stability, behavior near equilibria, bifurcation, etc.)
The framework of nonlinear evolutionary equations (developed, for example, in the text by Sell and You) allows one to view the examples listed above, and many others, as nonlinear ordinary differential equations on Banach spaces and use this convenient common framework for all of these equations to develop local existence, uniqueness, and regularity properties of solutions, continuity and smoothness of solutions with respect to initial data and parameters, global existence of solutions, and qualitative properties of solutions.
G. Sell and Y. You, Dynamics of evolutionary equations (2002), Springer.
Lecture notes developed by the instructor
Permission of Instructor