PDE Seminar, Academic Year 2007 - 2008

Next talk:

Monday, November 19: Positive solutions for reaction-diffusion system of PDE by degree theory.

Speaker: Anthony Leung

Abstract: Existence of positive solutions can be proved by upper-lower solution, monotone iteration, bifurcation and degree theory. In this talk we illustrate the proof by means of the degree theory method of cone index. We consider a prey-predator or competing species model with homogeneous (hostile) Dirichlet boundary data.The method expresses the condition for coexistence in terms of the principal eigenvalues of some related scalar linear equations. From these conditions one can readily see how coexistence depends on the relationship between the size of the environment domain, species growth and interaction rates.

Schedule:

Monday, Oct. 22, Nov. 5 and Nov. 19: Positive solutions for reaction-diffusion system of PDE by degree theory. Abstract
Speaker: Anthony Leung.


Monday, Oct. 8 and 15: A class of Nonlocal evolution equations. Abstract
Speaker: Guangyu Zhao.


Monday, Oct. 1: Translating Tridents. Abstract
Speaker: Xuan Hien Nguyen










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McMicken College of Arts and Sciences University of Cincinnati