2022威廉希尔

非线性分析、微分方程与动力系统系列报告

本期组织：吴事良、李善兵

主办单位：williamhill威廉希尔官网

基金资助：国家自然科学基金、陕西省杰出青年科学基金

联系人：李善兵手机：18700410622 E-mail:lishanbing@xidian.edu.cn

报告信息(以姓氏拼音为序)

Some New Degenerate Bifurcation Theorems and PDE Applications

刘萍 哈尔滨师范大学

摘要：In mathematical models from physical or biological applications, non-homogeneous states often arise as a result of symmetry breaking from homogeneous states, which is called bifurcation phenomenon. We consider a degenerate bifurcation scenario inwhich some transversality condition is not satisfied. In this case, we prove that, under some higher order transversality conditions, the local solution set of nonlinear equation near the bifurcation point consists of the line of trivial solutions, and two other solution curves. And we show some applications of these results in nonlinear partial differential equations arising from biological systems. This is joint work with Junping Shi.

报告人简介：刘萍，哈尔滨师范大学，教授，博士生导师。主要从事分歧理论及其在反应扩散方程中的应用的研究。黑龙江省新世纪优秀人才，黑龙江省领军人才梯队后备带头人，中国数学会理事，省工业与应用数学会常务理事，黑龙江省数学会常务理事。主持完成国家自然科学基金三项，黑龙江省基金二项。在JFA,JDE等高水平期刊发表论文20余篇。获省科技二等奖（第一名）1项，三等奖（第三名）1项，省教学成果一等奖（第二名）,黑龙江省数学会首届青年学术奖。出版教材3部。