哈尔滨师范大学偏微分方程方向
史峻平 王玉文
2005-2006研究计划
2007-2008研究计划
论文打字指南: 使用中文或英文LATEX系统
(并使用样本中格式, 特别注意论文方程号码引用方法)
(参考书: 《LATEX
入门与提高》，（第二版）：高等教育出版社, 2006 年5月出版, 陈
志杰，赵书钦，万福永编;
《LATEX2e
科技排版指南》，邓建松，彭冉冉，陈长松编，科学出版社)
中文LATEX系统: http://www.ctex.org/HomePage
希望使用CTEX(MiKTeX+WinEdT) http://www.ctex.org/CTeX
英文LATEX系统: 下面是我为威廉玛丽学院学生学习LATEX写的介绍:
LaTeX sample
file the
pdf printout of the LaTeX sample file
Quick tutorial for
LaTeX
论文样本1(Yuhua Zhao, Junping Shi and Yuwen
Wang)
论文样本2(Junping Shi, Ratnasingham Shivaji)
排版软件TEX/LATEX
入门
2005-2006
研究计划与进展:
刘
冠琦 (2011博) (email: lliuguanqi@163.com)
Reading:
Blat,
J.; Brown,
K. J. Bifurcation of steady-state solutions in
predator-prey and competition systems.
Proc.
Roy. Soc. Edinburgh Sect. A
97
(1984), 21--34. paper
Blat,
J.; Brown,
K. J. Global bifurcation of positive solutions
in some systems of elliptic equations.
SIAM
J. Math. Anal.
17
(1986),
no. 6, 1339--1353. paper
Dancer,
E. N. On positive solutions of some pairs of
differential equations.
Trans.
Amer. Math. Soc.
284
(1984),
no. 2, 729--743. paper
Dancer,
E. N. On positive solutions of some pairs of
differential equations. II.
J.
Differential Equations
60
(1985),
no. 2, 236--258. paper
Du,
Yihong; Shi,
Junping Some recent results on diffusive
predator-prey models in spatially heterogeneous environment.
Nonlinear dynamics and evolution equations, 95--135, Fields
Inst. Commun., 48, Amer. Math. Soc., Providence, RI,
2006. paper
Du,
Yihong; Shi,
Junping Allee
Effect
and Bistability
in a
Spatially Heterogeneous Predator-Prey Model (to appear in Transactions
of American Mathematics Society) paper
丁
慧 (2008硕) (email: dingyu119@163.com)
Reading:
(a) Shi,
Junping; Yao,
Miaoxin On a
singular nonlinear semilinear elliptic problem.
Proc.
Roy. Soc. Edinburgh Sect. A 128
(1998),
no. 6, 1389--1401. paper
(b) Dancer, E. Norman; Shi, Junping Uniqueness
of positive solution to sublinear semipositone
problem (Bulletins of
London Mathematical Society, Vol. 38, no. 6, 1033--1044, 2006.) paper
(c)
Clément,
Philippe; Sweers,
Guido Existence and multiplicity results for a
semilinear elliptic eigenvalue problem.
Ann.
Scuola Norm. Sup. Pisa Cl. Sci. (4)
14
(1987),
no. 1, 97--121. paper
付吉丽 (2008硕)
Reading:
(a) Sirakov,
BoyanNotions of sublinearity and superlinearity
for nonvariational elliptic systems.
Discrete
Contin. Dyn. Syst.
13
(2005),
no. 1, 163--174. paper
(b) Cui Renhao, Wang Yuwen, Shi Junping Uniqueness
of positive solution for a class of semilinear elliptic systems (to
appear in Nonlinear
Analysis: Theory, Methods & Applications).
(c) Hai,
D. D.; Shivaji,
R. An existence result on positive solutions
for a class of semilinear elliptic systems.
Proc.
Roy. Soc. Edinburgh Sect. A
134
(2004),
no. 1, 137--141. paper
(d) Hai,
D. D.; Shivaji,
R. An existence result on positive solutions
for a class of $p$-Laplacian systems.
Nonlinear
Anal.
56
(2004),
no. 7, 1007--1010. paper
(e)Hai,
D. D.; Shivaji,
R. Uniqueness of positive solutions for a
class of semipositone elliptic systems.
Nonlinear
Anal.
66
(2007),
no. 2, 396--402.paper
王亚南(2008硕)
Reading:
(a)
Oruganti,
Shobha; Shi,
Junping; Shivaji,
Ratnasingham Diffusive logistic equation with
constant yield harvesting. I. Steady states.
Trans.
Amer. Math. Soc.
354
(2002),
no. 9, 3601--3619 . paper
(b) Ambrosetti,
A.; Prodi,
G.On the inversion of some differentiable
mappings with singularities between Banach spaces.
Ann.
Mat. Pura Appl. (4) 93 (1972), 231--246.
paper
(c) Ambrosetti,
Antonio; Prodi,
Giovanni A primer of nonlinear analysis.
Cambridge
Studies in Advanced Mathematics, 34. Cambridge University
Press, Cambridge, 1993.
孙
丽男(2008硕) (Numerical, 数值计算)
Reading:
(a) Fuentes, et al Phys. Rev.
Lett. 91, 158104 (2003) paper
(b) Some textbook on numerical methods for PDEs
(c) Ikeda,
Hideo; Kondo,
Koji; Okamoto,
Hisashi; Yotsutani,
Shoji On the global branches of the solutions
to a nonlocal boundary-value problem arising in Oseen's spiral flows.
Commun.
Pure Appl. Anal.
2
(2003),
no. 3, 381--390. paper
(d) Kenkre, Physica A 2004, paper
刁瑞 (2008硕) (email: yiya-2005@163.com)
Reading:
(a) Cai, Guicai, On the heat flow for the two-dimensional Gelfand
equation. Nonlinear Anal. to
appear. paper
(b) Tello, J. Ignacio, Stability of steady states of the Cauchy problem
for the exponential reaction-diffusion equation. J. Math. Anal.
Appl. 324 (2006), no. 1, 381--396. paper
(c) Jiang,
Jifa; Liang,
Xing; Zhao,
Xiao-Qiang Saddle-point behavior for monotone
semiflows and reaction-diffusion models.
J.
Differential Equations
203
(2004),
no. 2, 313--330.paper
(d) Mizoguchi,
Noriko On the behavior of solutions for a
semilinear parabolic equation with supercritical nonlinearity.
Math. Z.
239
(2002),
no. 2, 215--229. paper
(e) Suzuki,
Ryuichi Asymptotic behavior of solutions of
quasilinear parabolic equations with supercritical nonlinearity.
J. Differential Equations
190
(2003),
no. 1, 150--181. paper
(2008硕)
Reading:
(a) Peng,
Rui; Wang,
Mingxin Pattern formation in the Brusselator
system.
J.
Math. Anal. Appl.
309
(2005),
no. 1, 151--166.paper
(b)
Brown, K. J.; Davidson,
F. A. Global bifurcation in the Brusselator
system.
Nonlinear
Anal.
24
(1995),
no. 12, 1713--1725. paper
(c) Erneux,
Thomas; Reiss,
Edward L. Brussellator isolas.
SIAM
J. Appl. Math. 43 (1983), no. 6,
1240--1246. paper
(d) Peña,
B.; Pérez-García,
C. Stability of Turing patterns in the
Brusselator model.
Phys.
Rev. E (3)
64
(2001),
no. 5, part 2, 056213, 9 pp. paper
学生已完成论文
- Liu,
Ping; Wang,
Yu-Wen The
generalized saddle-node bifurcation of degenerate solution.
Comment. Math. Prace Mat.
45
(2005),
no. 2, 145--150.
- Liu,
Ping; Wang,
Yuwen The
best generalised inverse of the linear operator in normed linear space.
Linear Algebra Appl.
420
(2007),
no. 1, 9--19.
- ZhaoYuhua, Wang Yuwen, Shi Junping Exact multiplicity of solutions
and S-shaped bifurcation curve for a class of semilinear elliptic
equations. Journal of
Mathematical Analysis and Applications 331(2007), no. 1,
263--278.
- Cui Renhao, Wang Yuwen, Shi Junping Uniqueness
of positive solution for a class of semilinear elliptic systems (to
appear in Nonlinear
Analysis: Theory, Methods & Applications).
- Duo Jia, Wang Yuwen, Shi Junping Structure
of the solution set of semilinear elliptic equations with asymptotic
linear nonlinearity (submitted)
- Liu Guanqi, Wang Yuwen, Shi Junping Existence
and nonexistence of
positive solutions of semilinear elliptic equation with inhomogeneous
strong Allee effect (submitted)
- Liu Ping, Wang Yuwen, Shi Junping Imperfect
transcritical and
pitchfork Bifurcations (submitted)
学报论文:
学习参考书目
线性泛函分析:
- 张恭庆,林源渠,泛函分析讲义,上册,北京,北京大学出版社,1987.
- 张恭庆 郭懋正,泛函分析讲义,下册,北京,北京大学出版社,1987
- Tosio Kato, Perturbation theory for linear operators.
Classics in Mathematics. Springer-Verlag, Berlin, (1995).
- Kosauku Yosida, Functional analysis. Sixth edition. Classics in
Mathematics. Springer-Verlag, Berlin-New York, (2003).
非线性泛函分析:
- 钟承奎, 非线性泛函分析引论（修
订版）兰州大学出版社
- Ambrosetti, Antonio; Prodi, Giovanni, A primer of nonlinear
analysis. Cambridge Studies in Advanced Mathematics, 34. Cambridge
University Press, (1995).
- Chang, Kung-Ching, Methods in nonlinear analysis. Springer
Monographs in Mathematics. Springer-Verlag, Berlin, (2005).
- Klaus Deimling, Nonlinear functional analysis. Springer-Verlag,
Berlin-New York, (1985).
- Louis Nirenberg, Topics in nonlinear functional analysis.
Courant Lecture Notes in Mathematics, 6. American Mathematical
Society, (2001).
偏
微分方程:
- 谷超豪 李大潜 陈恕行 郑宋穆 谭永基, 数学物理方
程（第二版） 高等教育出版社, 2002.
- 姜礼尚 陈亚淅 刘西垣 易法槐, 数学物理方程讲
义（第二版） 高等教育出版社, 2003
- 伍卓群 尹景学 王春明, 椭园与抛物型
方程引论 现代数学基础丛书, 科学出版社, 2003
- 叶其孝,李正元, 反应扩散方程引论. 科学出版社,1990.
- Lawrence Evans, Partial Differential Equations (Graduate Studies
in Mathematics, V. 19) American Mathematical Society,1998.
- David Gilbarg, Neil S.Trudinger, Elliptic Partial Differential Equations of Second Order. Classics
in Mathematics. Springer-Verlag, Berlin-New York, (2001).
常微
分方程和动力系统:
- 丁同仁 李承治, 常微分方程教程（第二
版） 高等教育出版社, 2004.
- Carmen Chicone, Ordinary Differential Equations with
Applications, Springer; 2 edition,, 2006.
- Daniel Henry, Geometric theory of semilinear parabolic equations.
Lecture Notes in Mathematics, 840.Springer-Verlag, Berlin-New York,
(1981).
- Lawrence Perko, Differential Equations and Dynamical Systems.
Springer; 3 edition, 2006.
- Stephen Wiggins, Introduction to applied nonlinear
dynamical systems and chaos. Texts in Applied Mathematics, 2.
Springer-Verlag, New York, (1990).
生物数学:
- Mathematical Biology, Vol. 1: An Introduction. By James
Dickson
Murray, Springer-Verlag, New York, (2002).
- Mathematical Biology, Vol. 2: Spatial Models and
Biomedical
Applications.
By James Dickson Murray, Springer-Verlag, New York, (2002).
- Mathematical Models in Biology. By Leah
Edelstein-Keshet,
McGraw-Hill,
Boston, (1988). SIAM, (2005).
- Elements of Mathematical Ecology. By Mark Kot,
Cambridge
University
Press, (2001).
- Diffusion and Ecological Problems: Modern Perspectives.
By
Akira
Okubo, Simon A. Levin, Springer-Verlag, New York, (2001).
- Essential Mathematical Biology, By Nicholas F.
Britton,
Springer-Verlag,
London, (2003).