Research Interaction Team Homepage
Applied Partial Differential Equations
Spring 2009

Weekly Meetings: 4:00pm - 4:50pm Mondays in MTH 1308
Team Directors: Stuart Antman (ssa"at"math) Sandra Cerrai (cerrai"at"math)
Manoussos Grillakis (mng"at"math) David Levermore (lvrmr"at"math)
Dionisios Margetis (dio"at"math) Antoine Mellet (mellet"at"math)
Eitan Tadmor (tadmor"at"cscamm) Konstantina Trivisa (trivisa"at"math)

Tentative Schedule

Date Speaker Topic
9 February J.T. Halbert Local Equilibrium for Brownian Particles
16 February David Levermore Classical Kinetic Equations, Gaussian Moment Closures, and Fluid Regimes
23 February Konstantinos Spiliopoulos Large Deviations Principle for Feller Diffusion Processes and Wave Front Propagation
2 March Stuart Antman Invariance and Computation for Hyperbolic Conservation Laws (postponed due to snow)
9 March Ioannis Markou The Rouse and Zimm Models in Polymer Dynamics
23 March Eitan Tadmor A New Approach to the 2D Pressureless Equations
30 March Dionisios Margetis Homogenization of Reconstructed Surfaces and Bose-Einstein Condensates
6 April Sandra Cerrai Quasipotentials and Exit Times
13 April Antoine Mellet Front Propagation in Heterogeneous Media
20 April Konstantina Trivisa Asymptotics and Navier-Stokes
27 April Manoussos Grillakis Bose-Einstein Condensates
4 May Arthur Cheng Two-Phase Euler
11 May Cynthia Bossard Mathematical Models for Stock Prices

RIT Plan

Research Focus: We will study mathematical aspects of applied partial differential equations. These might include well-posedness, long-time behavior, attractor dynamics, stability of coherent structures, asymptotic limits, and the relationship between chaos and stochasticity.

Graduate Prerequisites: Analysis (Math 630), or PDEs (Math 673), or ODEs (Math 414 or 670), or numerics (AMSC 666 or 660), or probability (STAT 600). Some knowledge of partial differential equations would be useful. Permission of a Team Director.

Undergraduate Prerequisites: Advanced calculus (Math 410) and differential equations (Math 246). Any of the following are useful but not required: complex variables (Math 463), ODE (Math 414), PDE (Math 462), computation (AMSC 460 or AMSC 466). Permission of a Team Director.

Graduate Program: Team members will make presentations either on readings of fundamental papers or book chapters, or on their own analytical and/or numerical investigations. When appropriate, these may be developed into more formal presentations for seminars, conferences, or publication. Team members will be asked to help mentor more junior team members.

Undergraduate Program: Same as above, as appropriate to the background of the student.

Work Schedule: Meetings will be held weekly.

RIT Participants

Faculty: Stuart Antman, Sandra Cerrai, Manoussos Grillakis, David Levermore, Dionisios Margetis, Antoine Mellet, Eitan Tadmor, Konstantina Trivisa
Postdocs: Arthur Cheng, Weiran Sun
Students: Avanti Athreya, Cynthia Bossard, J.T. Halbert, Ioannis Markou, Hyejin Kim, Karl Schmitt, Konstantinos Spiliopoulos

Topics Covered During Fall 2008

Date Speaker Topic
17 September Konstantinos Spiliopoulos Smoluchowski-Kramers Approximation for the Langevin Equation with Reflection
Sandra Cerrai Smoluchowski-Kramers Approximation for Stochastic PDEs
24 September Alexey Miroshnikov Radial Shocks in Elastodynamics
Stuart Antman Time-Asymptotics for Nonlinear PDEs
1 October Avanti Athreya Metastability for Nearly-Hamiltonian Systems
Weiran Sun Low Mach Number Limits for Dispersive Navier-Stokes Systems
8 October J.T. Halbert Dissipative Particle Dynamics
David Levermore Equations-of-State for Pressure
15 October Konstantinos Spiliopoulos Reaction-Diffusion Equations in Narrow Domains and Wave Front Propagation
22 October Avanti Athreya Large Deviations, Metastability, and Averaging for Diffusion Processes
29 October Arthur Cheng The Interaction between Nonlinear Koiter Shells and Viscous Fluids
5 November Alexey Miroshnikov A Time Approximation Scheme for the Equations of Elastodynamics in the Radial Case
12 November Konstantina Trivisa On the Dynamics of Multicomponent Flows (postponed to 20 November PDE Seminar)
19 November Sandra Cessai Fast Diffusion Asymptotics for Stochastic Reaction-Diffusion Equations with Boundary Noise
3 December Hyejin Kim Weak Convergence of D_v D_u - Processes
10 December Weiran Sun Low Mach Number Limits for Dispersive Navier-Stokes Systems

Updated 2 March 2009