Ohio State University Partial Differential Equations Seminar 

  Year 2018-2019

Time/Location: Thursdays 11:00 am- 11:55am / CH 240 (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 

Rachidi Salako 
(OSU) 
Spreading speeds and Traveling waves of chemotaxis models  Lam/Lou 

December 5 

No seminar 
() 
   

December 12 

No seminar 
() 
   

December 19 

No seminar 
() 
   

December 26 

No seminar 
() 
   
January 3 
No Seminar 
() 
   
January 10 
No Seminar 
() 
   
January 17 
No Seminar 
() 
   
January 24 
Adrian Lam 
(OSU) 
Dirac concentration in an integro-PDE model from adaptation   
January 31 
No Seminar 
() 
   
February 5 
CH240
Special Date 11am-noon
Emeric Bouin 
(Univ. Dauphine, France) 
About propagation in integro-dfferential equations   Lam/Lou 
February 7 
No Seminar 
() 
   
February 14 
No Seminar 
() 
   
February 21 
No Seminar 
() 
   
February 28 
No Seminar 
() 
   
March 7 
No Seminar 
() 
   
March 12 
Joint with Analysis
11:30am; CH240
Anders Bjorn 
(Linkoping University, Sweden) 
Boundary regularity for the nonlinear p-parabolic and porous medium equations  Lang 
March 14 
No Seminar 
() 
   
March 21 
No seminar 
() 
   
March 28 
Judith Miller 
(Georgetown) 
  Lam/Lou 
April 4 
Peiyong Wang 
(Wayne State) 
  Lou 
April 11 
Robert L Jerrard 
(U. Toronto) 
  Guan 
April 18 
No seminar 
() 
   
April 25 
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

Rachidi Salako (Nov 28, 2018)

Title: Spreading speeds and Traveling waves of chemotaxis models
Abstract: Chemotaxis described the oriented movements of mobile species in response to chemical signals by moving along gradient of the chemical substance, either toward higher concentration or away from it. Mathematical models describing chemotaxis have gained more interests over the last few decades. It is well known that such mathematical models exhibit very colorful dynamics. In this talk, we study the spreading speeds of solutions with compactly supported initials, and the existence/non-existence of Traveling wave solutions of the classical Keller-Segel chemotaxis models with logistic sources on R^N. We shall also discuss about some interesting problems.

Adrian Lam (Jan 24, 2019)

Title: Dirac concentration in an integro-PDE model from adaptation
Abstract: We consider a mutation-selection model of a population structured by the spatial variables and a trait variable which is the diffusion rate. Competition for resource is local in spatial variables, but nonlocal in the trait variable. We establish the existence and asymptotic profile of a steady state solution. Our result shows that in the limit of small mutation rate, the solution remains regular in the spatial variables and yet concentrates in the trait variable and forms a Dirac mass supported at the lowest diffusion rate. Similar result was independently obtained by B. Perthame and T. Souganidis via an elegant method. I will present a sketch of proof blending the arguments of both papers. This is joint work with Yuan Lou and Wenrui Hao (Penn State).

Emeric Bouin (Univ. Dauphine, Paris) (Feb 5, 2019)

Title: About propagation in integro-dfferential equations
Abstract: In this talk, I will review and discuss various results about finite and accelerated propagation in integro differential equations of KPP type. This will include a Bramson logarithmic delay when the jump kernel is thin, and a rate of acceleration for fat tailed kernels.

Judith Miller (Georgetown) (Mar 280, 2019)

Title:
Abstract:

Robert L Jerrard (Toronto) (Apr 10, 2019)

Title:
Abstract:

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