Two seminars at Center for Mathematical Sciences, September 24, Thursday,

报告（一）

时间：Sept 24, Thursday,10am-11am

地点：Center for Mathematical Sciences, Room813 (创新研究院恩明楼813室)

报告人：Yusuke Asai（nstitut fur Biostatistik und mathematische Modellierung, Klinikum und Fachbereich Medizin, Goethe-Universitat Frankfurt）

标题：Mathematical modeling by random ordinary dierential equations and their applications in biology and medicine.

摘要：Random ordinary differential equations (RODEs) are ordinary differential

equations which have a stochastic process in their vector field functions.

They have been used in a wide range of applications and play an important

role in the theory of random dynamical systems, however, they have been

long overshadowed by SDEs.

In this talk, Firstly, I will give an overview of RODEs. After a brief introduction

of RODEs, numerical methods for RODEs with It^o diffusion can

be constructed via RODE{SODE transformation and It^o{Taylor schemes

as well as linear multi-step methods are derived. In addition, numerical

methods for RODEs with the structure will be discussed.

The developed numerical methods will be applied to biological and medical

models, e.g., hepatitis C virus kinetic model, tumor growth model and

pattern formation, and the accuracy of the methods as well as their computational

costs will be compared.

报告（二）

时间：Sept 24, Thursday, 11am-12noon

地点：Center for Mathematical Sciences, Room813 (创新研究院恩明楼813室)

报告人：Daomin Cao （Institute for Applied Mathematics Chinese Academy of Sciences）

标题：Pohozaev type identities and their applications in partial differential equations