Math 741. Topics in Partial Differential Equations: Blow-up for nonlinear wave equations.
- Fall 22 - Hans Lindblad

I will teach a topics class in PDE, mostly going over some recent blow-up results for nonlinear wave equations by Merle and others. Many interesting equations from Physics can be written as systems of Nonlinear wave equations. One can always show that these have local solutions for some time. The ultimate goal for many physical equations is to prove existence of global solutions for all times. However, apart from in special cases such as small perturbations around a steady state one can not not prove that there are global solutions. In fact the solutions may develop singularities or blow up at some finite time, after which no regular solution exist anymore. This blow-up can either be a real phenomena in nature, such as development of black holes in general relativity or it can be an indication that nature is non longer accurately described by the model. In either case we would like to avoid blow-up. It is therefore important to study how blow-up can occur for nonlinear wave equations.

The lectures are MW 1.30-2.45 in Krieger 406.

wk  date  Monday  Wednesday  Friday
  1  8/29      
  2  9/5  Holiday    
  3  9/12      
  4  9/19      
  5  9/26      
  6  10/3      
  7  10/10  moved to Tuesday 10/11    
  8  10/17      
  9  10/24      
10  10/31      
11  11/7      
12  11/14      
13  11/21    No Class  No Class
14  11/28