中国计量学院马满军教授来我校讲学
发布时间：2015-02-07
2月5日上午，中国计量学院马满军教授来我校讲学，在数学楼五楼学术讨论室作题为“Diffusion, Chemotaxis and Pattern Formation: A Case Study Via Topological method and Asymptotic Analysis”学术报告。
马满军，中国计量学院教授，硕士导师，主要研究领域为微分方程与动力系统理论及其应用。
2005年毕业于湖南大学，获应用数学专业博士学位；2007-2008年在美国San Diego 州立大学动力系统研究中心做博士后研究；2008年至2014年多次应邀访问加拿大纪念大学数学与统计学系及香港理工大学应用数学系。
以第一作者在Journal of Differential Equations、SIAM Journal on Applied Mathematics、Discrete and Continuous Dynamical Systems及Physical Review A等国内外重要学术刊物发表论文30余篇，其中SCI收录20余篇；主持研究国家自然科学基金面上项目、教育部留学归国人员科研启动基金各一项；参与研究科技部973项目重大基础研究前期研究专项一项。
clas�Loo� �z le="text-autospace:ideograph-other; text-align:left; line-height:15.0000pt; " >stable stationary solutions in virtue of the estimation of the leading term of
principal eigenvalues. We show that all bifurcations except the one
at the first location of the bifurcation parameter are unstable, and
if the pattern is stable, then its principal wave mode must be a positive
integer which minimizes the bifurcation parameter.
abstract: Pattern formation is quite common to be seen in natural
environment such as the formation of animal skin spots. Besides the
pioneering explanation of Alan Turing in 1952 in terms of reaction
diffusion equations, recently chemotaxis is thought as another
important factor in the process of pattern formation. In this talk,
by a case study we analyze the effect of diffusion and chemotaxis in
a volume-filling model. The existence of Turing Pattern can be proved
by topological-degree method. Via an asymptotic analysis, we derive an
explicit formula for the stationary patterns. Moreover, based on
this explicit formula, we establish the stability criteria and
find a selection mechanism of principal wave modes for the
stable stationary solutions in virtue of the estimation of the leading term of
principal eigenvalues. We show that all bifurcations except the one
at the first location of the bifurcation parameter are unstable, and
if the pattern is stable, then its principal wave mode must be a positive
integer which minimizes the bifurcation parameter.