Mathematics Department Seminar

 
 

Computational and Applied Mathematics Seminar

Spring 2019

Mondays at 4:10 p.m. in 401 Carver


The CAM Seminar is organized in the ISU Mathematics Department. It brings speakers from inside and outside of ISU, raising issues and exchanging ideas on topics of current interest in the are of computational and applied mathematics.

Archive of previous CAM seminars

 



3/04

Title: Recent Results for the 3D Quasi-Geostrophic System: Boundary Conditions and Non-Uniqueness

Matthew Novack
University of Texas, Austin

ABSTRACT:  The 3D Quasi-Geostrophic system is a set of equations used in meteorology to describe the evolution of the atmosphere. The surface quasi-geostrophic equation (2D SQG) is a well-studied special case where the atmosphere above the earth is at rest. In this talk, we will discuss a pair of recent results, the first of which derives the physical boundary conditions for the 3D model and constructs global in time weak solutions. The second result shows the non-uniqueness of weak solutions to the 3D model via a convex integration argument.


3/11

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3/18

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3/25

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4/01

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4/08

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4/15

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4/22

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4/29

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5/06

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1/14

Title: Moving Mesh simulation of contact sets in two dimensional models of elastic-electrostatic deflection problems

Yufei Yu
University of Kansas

ABSTRACT: Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections that model micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial differential equation and the contact events occur in this system as finite time singularities. In this talk, I will talk about an adaptive moving mesh strategy, which is developed based on a moving mesh partial differential equation that dynamically relocates a fixed number of mesh points to increase density where the singularities take place. To complement this computational tool, a singular perturbation analysis is used to develop a geometric theory for predicting the possible contact sets. Numerical results that demonstrate the validity of these two approaches will be presented.


1/21

University holiday


 


1/28

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2/04

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2/11

Title: Nonconvexity and Compact Containment of Mean Value Sets for General Elliptic Operators

Niles Armstrong
Kansas State University

ABSTRACT:  In his Fermi Lectures on the obstacle problem, Caffarelli stated a mean value theorem for second order uniformly elliptic divergence form operators with the form $L:=D_i a^{ij}(x) D_j.$ This theorem is a clear analog to the standard mean value theorem for Euclidean balls for the Laplacian, with the only difference being the sets over which the averages are taken. I will discuss the initial regularity results that were known for these sets, show a new compact containment result, and finally give an example of an operator with smooth coefficients and nonconvex mean value sets.


2/18

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2/25

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