【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室)

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

**A****bstract****: **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

**A****bstract****:** 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

**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.