Ohio State University Partial Differential Equations Seminar 

  Year 2018-2019

Time/Location: Wednesdays 11:00 am- noon / MW 154 (unless otherwise noted)

Schedule of talks:


 
TIME  SPEAKER TITLE HOST

August 29 

Ni Xiang 
(Hubei University, China) 
The Neumann problem for fully nonlinear elliptic equations on Riemannian Manifolds  Guan 

September 5 

No seminar 
() 
   

September 12 

No seminar 
() 
   

September 19 

No seminar 
() 
   

September 26 

No seminar 
() 
   

October 3 

Chris Klausmeier 
(Michigan State) 
Theoretical Approaches to Phytoplankton Ecology   Lam 

October 10 

Chris Cosner 
(U. Miami) 
The role of nonlocal information in the dispersal of animals in spatiotemporally varying environments  Lam/Lou 

October 12 
Special MW100A

Wenxian Shen 
(Auburn) 
Dynamics in Chemotaxis Models with Logistic Source  Lam/Lou 

October 17 

No seminar 
() 
   

October 24 

No seminar 
() 
   

October 31 

No seminar 
() 
   

November 7 

Avner Friedman 
(OSU) 
Rheumatoid arthritis: a mathematical model    

November 14 

No seminar 
() 
   

November 21 

No seminar 
() 
   

November 28 

No seminar 
() 
   

December 5 

No seminar 
() 
   

December 12 

No seminar 
() 
   

December 19 

No seminar 
() 
   

December 26 

No seminar 
() 
   
January 2 
No Seminar 
() 
   
January 9 
No Seminar 
() 
   
January 16 
No Seminar 
() 
   
January 23 
No Seminar 
() 
   
January 30 
No Seminar 
() 
   
February 6 
No Seminar 
() 
   
February 13 
No Seminar 
() 
   
February 20 
No Seminar 
() 
   
February 27 
No Seminar 
() 
   
March 6 
No Seminar 
() 
   
March 13 
No Seminar 
() 
   
March 20 
No seminar 
() 
   
March 27 
No Seminar 
() 
   
April 3 
No seminar 
() 
   
April 10 
Robert L Jerrard 
(U. Toronto) 
  Guan 
April 17 
No seminar 
() 
   
April 24 
No Seminar 
() 
   

Abstracts

Ni Xiang (Aug 29, 2018)

Title: The Neumann problem for fully nonlinear elliptic equations on Riemannian Manifolds
Abstract: Fully nonlinear partial differential equations play important roles in geo- metric problems, such as curvature equations in classical geometry and the Yamabe problems on manifolds. A key to understand these equations is to establish a priori estimates for these equations. The Dirichlet problems have received much attention. In this talk we report some recent results joint with Professor Guan Bo for the Neu- mann problem of fully nonlinear elliptic equations on Riemannian manifolds. We try to delete the structural condition for the Neumann boundary in deriving estimates for second derivatives. And we use a priori estimates and blow-up methods to derive the gradient estimates.

Chris Klausmeier (Oct 3, 2018)

Title: Theoretical Approaches to Phytoplankton Ecology
Abstract: Phytoplankton, the microscopic primary producers in lakes and oceans, are an ideal system for doing theoretical ecology. In this talk I will talk about three dimensions in which phytoplankton show intriguing patterns: in space, in time, and in the space of functional traits. In space, we focus on the vertical distribution of phytoplankton in the water column. Phytoplankton require light and nutrients to grow, but these essential resources often form contrasting gradients with depth. We use reaction-diffusion-advection models along with game theoretical approaches to figure out how phytoplankton resolve this problem. In time, plankton communities are regularly driven away from equilibrium by the changing of the seasons. We use forced differential equation models and analytical approximations to study the dynamics of the seasonal succession of species. In trait-space, we use trait-based modeling techniques adapted from evolutionary game theory to understand the emergence and maintenance of biodiversity in ecological communities. This is joint work with E. Litchman.

Chris Cosner (Oct 10, 2018)

Title: The role of nonlocal information in the dispersal of animals in spatiotemporally varying environments
Abstract: Recent research on reaction-advection-diffusion models and related integro-differential models for animal movement has shown that in spatially varying but temporally constant environments, animals can achieve an evolutionarily stable spatial distribution on the basis of purely local information about the environment. However, there is empirical evidence that in some situations animals use nonlocal information to inform their movements. Numerical computations give evidence that by using nonlocal information on how to advect and diffuse, animals can improve their success at foraging in some spatiotemporally varying environments. Furthermore, in time periodic environments, it is sometimes possible for animals to achieve an evolutionarily stable spatial distribution by means of diffusion and advection, but to do so requires the use of nonlocal information. This talk will give some background and present some recent results on these topics. The modeling and analysis will be done in the mathematical framework of reaction-advection-diffusion equations.

Wenxian Shen (Oct 12, 2018)

Title: Dynamics in Chemotaxis Models with Logistic Source
Abstract: The current talk is concerned with the asymptotic dynamics in chemotaxis models with logistic source. In particular, I will present some of my recent joint works on the asymptotic dynamics of the following three types of chemotaxis models: chemotaxis models with time and space dependent logistic source on bounded domains; chenotaxis models with logistic source on bounded moving domains with a free boundary; and chemotaxis models with logistic source on the whole space.

Avner Friedman (Nov 7, 2018)

Title: Rheumatoid arthritis: a mathematical model
Abstract: A joint is a structure that connects two parts of the skeleton; in particular, the synovial joint is a joint where two bones are connected. This joint consists of cartilage (as cushion) at each bone-end, synovial fluid (as shock absorber when bones are rotated) and synovial membranes between the cartilages and the fluid. Rheumatoid arthritis (RA) is an autoimmune inflammatory degenerative disease of the synovial joints. The inflammations begins in the synovial membrane by immune cells, and it leads to the destruction of the cartilage. There are two million Americans with RA. In this talk, I will present a novel mathematical model of RA. The model is presented as a system of PDEs in the three compartments of the synovial joint. As the cartilage layer degrades it becomes thinner, and its boundary that is in contact with the synovial membrane is moving in time as a “free boundary.” There is no cure to RA, but drugs are used to try slow the progression of the disease. I shall use the model to evaluate the efficacy of several approved drugs, combination of drugs, and experimental drugs. Finally, I will briefly present open mathematical problem in PDE with free boundary that are associated with the model. This a joint work with Nicola Moise from the medical school in Bucharest, Romania

Robert L Jerrard (Apr 10, 2019)

Title:
Abstract:

This page is maintained by Adrian Lam.
Does the page seem familiar?