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Math Colloquium: A Stable Manifold Theorem for a Class of Degenerate Evolution Equations and ...
Start Date: 3/6/2017Start Time: 3:00 PM
End Date: 3/6/2017End Time: 4:00 PM

Event Description
Kevin Zumbrun, Indiana University

 

Abstract: We establish a Stable Manifold Theorem, with consequent exponential decay to equilibrium, for a class of degenerate evolution equations $Au'+u=D(u,u)$ with A bounded, self-adjoint, and one-to-one, but not invertible, and $D$ a bounded, symmetric bilinear map. This is related to a number of other scenarios investigated recently for which the associated linearized ODE $Au'+u=0$ is ill-posed with respect to the Cauchy problem. The particular case studied here pertains to the steady Boltzmann equation, yielding exponential decay of large-amplitude shock and boundary layers.
Contact Information:
Name: Ronald Perline
Email: rperline@math.drexel.edu
Location:
Korman Center, Room 245, 15 South 33rd Street, Philadelphia, PA 19104
Audience:
  • Everyone
    		•

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