WAKE FOREST UNIVERSITY
DEPARTMENT OF MATHEMATICS & STATISTICS
Wake Forest University
Thursday, September 26th, 2019
Carswell Hall, Room 101
Abstract: Nonlinear PDEs are difficult to solve explicitly. Therefore, mathematicians are interested in discovering properties about the solutions, by using and developing analytical techniques. The first questions we need to answer are: ‘do solutions exist?’, ‘are solutions unique?’, and ‘do the solutions depend continuously upon the initial data?’. If the answer is yes to all three questions, we say the initial value problem for the PDE is well-posed. We will explore the well-posedness arguments for three PDEs, comparing and contrasting the techniques used based on the operators in each PDE.