講座題目:Global bifurcation theory for Fredholm operators and an application to chemotaxis systems
講座人:王學(xué)鋒 教授
講座時間:14:30
講座日期:2014-12-12
地點:長安校區(qū) 文津樓數(shù)學(xué)與信息科學(xué)學(xué)院多功能廳
主辦單位:數(shù)學(xué)與信息科學(xué)學(xué)院
講座內(nèi)容:In this talk, I will introduce a relatively newglobal bifurcation theory for Fredholm operators, due to Fitzpatric,Pejsachowicz and Rabier, that generalizes Rabinowitz theorem. Itdoes not require the conversion of the PDE to a compact perturbation of theidentity; and as a special case of the theory, by adding a Fredholmnesscondition on the nonlinear operator, the Crandall-Rabinowitz local bifurcationtheorem becomes a global bifurcation theorem. I will also introducethe unilateral bifurcation theorem, and sufficient conditions for a ellipticsystem with general boundary conditions to be Fredholm with 0 index, due toJunping Shi and myself.
Finally, I will show how to apply the globalbifurcation theory to a class of chemotaxis systems, obtaining steadystates with striking features such as spikes and transition layers.