PDE/Applied seminar: John Helms (UCSB), 'Nonlinear wave equations in 3 spatial dimensions (part II)'

Event Date: 

Friday, February 15, 2013 -
3:00pm to 4:00pm

Event Location: 

  • 4607B South Hall

Event Contact: 

Carlos Garcia-Cervera

Email: cgarcia@math.ucsb.edu

Following up on last week's talk, we are continuing our discussion on nonlinear wave equations in 3 spatial dimensions. Now we will consider small-data solutions wave equations of the form $( partial_t^2 - Delta ) u = Q(u,u',u'')$ where $Q$ is the nonlinearity which is quadratic in $u$ and $u'$ and linear in $u''$. Instead of considering the case where the spatial domain is $mathbb{R}^3$, we will now be working in an exterior domain, $mathbb{R}^3 backslash mathcal{K}$, where $mathcal{K}$ is a smooth, bounded domain. We will discuss how Klainerman's method of invariant vector fields can be extended to work in exterior domain problems. The one of our main goals is to obtain the exterior domain analogs of classical results that are already known when the spatial domain is $mathbb{R}^3$.