For more information about this meeting, contact Hope Shaffer, Jinchao Xu, Kris Jenssen.
|Title:||Weakly Nonlinear-Dissipative Approximations of Hyperbolic-Parabolic Systems with Entropy|
|Seminar:||Computational and Applied Mathematics Colloquium|
|Speaker:||David Levermore, University of Maryland|
|Hyperbolic-parabolic systems have spatially homogeneous
stationary solutions. When the dissipation is weak, one can derive
weakly nonlinear-dissipative approximations that govern perturbations
of these solutions. These approximations are quadratically nonlinear.
Up to a linear transformation, they are independent of the dependent
variables used to express the original system. When the original
system has an entropy, the approximation is formally dissipative in a
natural Hilbert space. We show that under a mild structural hypothesis,
this approximation has global weak solutions for all initial data in that
Hilbert space. This theory applies to the compressible Navier-Stokes
system. The resulting approximate system is an incompressible
Navier-Stokes system coupled to equations that govern the acoustic modes.
The solution of this approximate system is unique if the incompressible
modes are uniquely determined.|
Room Reservation Information
|Date:||04 / 04 / 2008|
|Time:||03:35pm - 04:25pm|