Events
Department of Mathematics and Statistics
Texas Tech University
 | Monday
Sep. 16
|
| Algebra and Number Theory
No Seminar
|
We study the anisotropic Forchheimer-typed flows for compressible fluids in porous media. The first half of the paper is devoted to understanding the nonlinear structure of the anisotropic momentum equations. Unlike the isotropic flows, the important monotonicity properties are not automatically satisfied in this case. Therefore, various sufficient conditions for them are derived and applied to the experimental data. In the second half of the paper, we prove the existence and uniqueness of the steady state flows subject to a nonhomogeneous Dirichlet boundary condition. It is also established that these steady states, in appropriate functional spaces, have local Hölder continuous dependence on the forcing function and the boundary data. This is a joint work with Thinh Kieu (University of North Georgia, Gainesville Campus.)
Abstract. Lorentz electrodynamics with point charges is notoriously ill-defined. So is quantum electrodynamics (QED). Already in the 1930s Max Born suggested that the problems could be overcome by changing the ``law of the pure ether'' from Maxwell's and Lorentz' linear identification of E with D and of B with H, into some nonlinear algebraic relation. Subsequently he was joined by L. Infeld who contributed an insight that led to the well-known Born-Infeld (BI) law. In 1940 Fritz Bopp picked up on Born's ideas and suggested a linear higher-derivative law as an alternative. This was independently suggested by Lande and Thomas, and picked up by Podolsky (BLTP), and implemented into QED by Feynman. A few years ago, the joint initial value problem for BLTP electrodynamics was shown to be locally (in time) well-posed. The analogous result for BI electrodynamics is expected but no proof is in sight. The talk will survey the conceptual problems and outline the gist of the proof of the local well-posedness of the BLTP initial value problem.
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room MATH 011 (basement)
ZOOM details:
- Choice #1: use this link
Direct Link that embeds meeting and ID and passcode.
- Choice #2: join meeting using this link
Join Meeting, then you will have to input the ID and Passcode by hand:
* Meeting ID: 979 1333 6658
* Passcode: Applied (Note the capital letter "A")
 | Thursday
Sep. 19
6:30 PM
MA 108
|
| Mathematics Education
Math Circle
Aaron Tyrrell
Mathematics and Statistics, Texas Tech University
|
Math Circle Fall Poster
abstract noon CDT (UT-5)
Zoom link available from Dr. Brent Lindquist upon request.