The study of nonlinear partial differential equations plays an ever increasing role in science, and many fundamental mathematical aspects need to be developed further in order to answer important questions for applications in branches as different as physics, biology, and economy to mention just a few. The present project brings together experts in these domains from China and Switzerland with the goal to exchange ideas, consolidate the present knowledge, and, most important, foster new collaborations between the participating Universities.

Renmin University of China has recently established the Institute for Mathematical Sciences (IMS), led by Professor Yuan Lou. Professor Lou and 5 postdocs at IMS work in the area of Partial Differential Equations, including reaction-diffusion equations, calculus of variation and nonlinear analysis. More details of the research group at IMS can be found at the website http://ims.ruc.edu.cn/more2.php?cid=2.

The research interest of Yaobin Ou is in the mathematical theory of partial differential equations from fluid mechanics, in particular on the well posedness of free boundary problems and singular limits (low Mach number limit and related problems).

The research group of Peter Wittwer will contribute to the collaboration with expertise closely related to these research interests. The group has been working as well on reaction diffusion problems as on problems in fluid mechanics and singular limits.

The research group of Zhengguang Guo also has expertise in the question of regularity of solutions of nonlinear partial differential equations. He has in the past visited the DPT at Geneva Universities at several occasions (mainly financed SSSTC ). His contribution has been crucial in order to establish contact and bring together the research groups at the IMS and the DPT who participate in this project.

The mathematical approaches to the problems of these research groups are however complementary in many ways and the collaboration therefore promises to be most interesting and very rich, since different ideas and techniques will be brought together.

The Institute for Mathematical Sciences will serve as the leading platform for the project. The start of the project will therefore be in the form of a kick off meeting at Renmin University which will bring together all the participants of the project. This will allow to exchange ideas and to establish collaboration on concrete mathematical problems. Subsequent visits of the Chinese partners to the University of Geneva will allow to push these projects forward and will tighten the link between the participating institutions. It will at the same occasion allow to define the future collaboration between the institutions.

We expect that as a result of this project a permanent collaboration between the participating Institutes will be established.

**Participants : **

- UNIGE:
- Prof. Peter Wittwer, Faculty of Science, Department of Theoretical Physics

- Renmin
- External partner:
- Dr Zhengguang Guo, Wenzhou University - College of Mathematics and Information Science