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【Coll. 0626/27】PDE Mini-Symposium
时间:2018-06-27  浏览:208次

Schedule for mini-symposium at Renmin University

316 Environmental Building (环境楼316)

June 26, Afternoon

14:00 - 14:45 Bei Hu

14:45 - 15:30 Jingli Ren

15:30 - 16:00 Discussion & Tea break

16:00 - 16:45 Emeric Bouin

16:45 - 17:30 King-Yeung Lam

17:30 - 18:00 Discussions

18:00 Dinner

June 27, Morning

08:00 - 08:45 Stephen Cantrell

08:45 - 09:30 Tian Xiang

09:30 - 10:00 Discussion & Tea break

10:00 - 10:45 Maolin Zhou

10:45 - 11:30 Xiulan Lai

11:30 - 12:00 Discussion

12:00 Lunch

June 28,All day

free to discuss.

June 29, All day

free to discuss.

Tile and abstract

Emeric Bouin

CEREMADE - Université Paris-Dauphine

bouin@ceremade.dauphine.fr

Title: Large deviations for velocity-jump processes

Abstract: In this talk, I will present some results concerning the study of large deviations for velocity jump processes from a PDE point of view. The Chapman-Kolmogorov equation of the process being a kinetic equation, I will show how to perform an Evans-Souganidis/Freidlin type of approach directly at the kinetic level. The talk will also underline the differences between the results we obtain, and the classical results obtained for the macroscopic limit of the process (the heat equation).

Stephen Cantrell

Department of Mathematics, University of Miami

rsc@math.miami.edu

Title: Resident-Invader Dynamics in Infinite Dimensional Systems

Abstract: Motivated by evolutionary biology, we study general infinite-dimensional dynamical systems involving two species - the resident and the invader. Sufficient conditions for competition exclusion phenomena are given when the two species plays similar strategies. Those conditions are based on invasibility criteria, for instance, evolutionarily stable strategies in the framework of adaptive dynamics. This type of question was first proposed and studied for a class of ordinary differential equations in (S. Geritz et al., J. Math. Biol., 2002) and (S. Geritz,J. Math. Biol. 2005). We extend and generalize previous works in two directions. First, we consider analytic semiflows in infinite-dimensional spaces. Secondly, we device an argument based on Hadamard’s graph transform method that does not depend on the monotonicity of the two-species system. Our results are applicable to a wide class of reaction-diffusion models as well as models with nonlocal diffusion operators.

Bei Hu

Department of Applied Computational Mathematics and Statistics

University of Notre Dame

b1hu@nd.edu

Title: A Free Boundary Problem for Corporate Bond with Credit Rating Migration

Abstract: A free boundary model for pricing a corporate bond with credit rating migration is studied. Some interesting properties, as well as numerical examples, numerical schedule convergence rate, will be presented.

King-Yeung Lam

Department of Mathematics, Ohio State University

lam.184@osu.edu

Title: Invasion of Open Space by Two Competing Species
Abstract: In this talk I will discuss the spreading properties of two competing species on the real line when the initial values are null or exponentially decaying in a right half-line. In the case of compactly supported initial values, we prove that the first species spreads with the KPP speed of the single species, whereas the speed of the second species can be given by an exact formula depending on the speed of the first species. This is joint work with Leo Girardin (Paris VI). If time allows, I will also talk about some recent progress obtained with Qian Liu (Renmin Univ. of China).

Xiulan Lai

Institute for Mathematical Sciences, Renmin University of China

xiulanlai@ruc.edu.cn

Title: Mathematical modeling about cancer combination therapy with oncolytic virus and checkpoint inhibitor

Abstract: In this talk we consider a combination therapy with oncolytic virus and a checkpoint inhibitor, anti-PD-1. We evaluate the efficacy of the combination therapy in terms of the tumor volume at some later time, for example, 6 months from initial treatment. Since T cells kill not only virus-free cancer cells but also virus-infected cancer cells, the following question arises: Does increasing the amount of the checkpoint inhibitor always improve the efficacy ? We address this question, by a mathematical model consisting of a system of partial differential equations. We use the model to construct, by simulations, an efficacy map in terms of the doses of the checkpoint inhibitor and the OV injection. We show that there are regions in the map where an increase in the checkpoint inhibitor actually decreases the efficacy of the treatment. We also construct efficacy maps with checkpoint inhibitor vs. the replication potential of the virus that show the same antagonism, namely, an increase in the checkpoint inhibitor may actually decrease the efficacy. These results have implications for clinical trials.

Jingli Ren

Department of Mathematics and Statistics, Zhengzhou University

renjl@zzu.edu.cn

Title: Information diffusion in online social network
Abstract: In this talk, we present three models of information diffusion in ONS and discuss their dynamical behavior.

Tian Xiang

Institute for Mathematical Sciences, Renmin University of China

txiang@ruc.edu.cn

Title: On global and blow-up solutions for a short-ranged chemical signaling loop

Abstract: In this talk, we consider the global boundedness and blow-up of solutions to a two-species and two-stimulus chemotaxis model, in which the process of the species results in a short-ranged chemical signaling loop. Explicit conditions on the initial data are given for the existence of simultaneous global boundedness and simultaneous finite-time blow up of classical solutions. More precisely, since the dynamics of one species are expected to be essentially determined by the other through this chemotactic signaling loop between two cell types, we find that only smallness of mass of one species implies global solvability, whereas, largeness of masses induce blow-up to occur. These in particular improve the known existing knowledge where smallness of total masses of both two species is required. This is a joint work with K. Lin from Southwestern University of Finance and Economics.

Maolin Zhou

University of New England at Armidale

mzhou6@une.edu.au

Title: Long time behaviors of the Fisher-KPP equation in the river network

Abstract: In this work, we consider the propagation phenomena in the river with two or three branches and the effect of water speed on it. And we give out a classification of the asymptotic behaviors of solutions for different cases. This is a joint work with Y. Du, B. Lou and R. Peng.