Applied PDE Seminar
Department of Mathematics, Florida State U., Fall 2013
Tuesday 3:30-4:20, LOV104
This page is maintained by
Dr. Xiaoming WANG
We are interested in partial differential equations and their applications in a very broad sense (including modelling, analysis, computation and more).
Each registered student must give a presentation.
All are welcome.
- Date: Tue. Aug. 27, 2013
Speaker: Organizational meeting
- Date: Tue: Sept. 3rd, 2013
Speaker: Xiaoming Wang, FSU Math
Title: Monotone operator
Solution to "suitable" finite dimensional approximate problem of an infinite dimensional problem does not necessarily converge. We show that this is not an issue if the equation/problem under investigation has some kind of monotonicity and coercivity. In particular, we will prove the Minty-Browder theorem and discuss its applications to the analysis of PDEs.
- Date: Tue: Sept. 10th, 2013
Speaker: Daozhi Han, FSU Math
Title: Monotone numerical schemes
Many times it is desirable to design monotone numerical scheme for PDE models.
Minty-Browder Theorem guarantees the (unique) solvability of the scheme which is a sort after feature.
Han will present examples of such schemes and verify that the monotonicity and other conditions (coercivity ...).
Two interesting papers
You may also find the following two books on multi-scale problems quite readable
- Hydrodynamic models of self-organized dynamics: derivation and existence theory
by Pierre Degond, Jian-Guo Liu, Sebastien Motsch, and Vladislav Panferov
- The restaurant at the end of the random walk: recent
developments in the description of anomalous transport by fractional dynamics,
by Ralf Metzler1 and Joseph Klafter,
J. Phys. A: Math. Gen. 37 (2004) R161b
The following book might be of interest to you if data assimilation for chaotic system with sparse observations is a concern
- Principles of Multiscale Modeling by Weinan E, published by Cambridge
- Multiscale Methods: Averaging and Homogenization (Texts in Applied Mathematics) by Grigoris Pavliotis and Andrew Stuart, published by Springer.
- Filtering Complex Turbulent Systems by Andrew Majda and John Harlim, published by Cambridge University Press
Please contact Xiaoming Wang
if you have any questions regarding this seminar.