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穆春来

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姓名：穆春来
目前身份：
担任导师情况：
学位：
学术头衔：

博士生导师
职称：-
学科领域：

数理逻辑与数学基础
研究兴趣：偏微分方程

个人简介

　穆春来，教授、博士生导师。研究方向：偏微分方程。对带有摄动位势的波方程解的估计，非线性抛物方程解的爆破速率，第二临界指数和渐近性态以及偏泛函微分方程振动性等问题都作出了有影响的工作。已在"J. Diff. Eqs"、"Comm. PAA"、"Comp. Math. Appl"、"JMAA"、"Nonlinear Anal."、"Dyna. Systems: An International Journal"、"Appl. Math. Letters"、"数学年刊"等国内外重要期刊上发表论文40余篇，其中SCI 14篇。承担了国家自然科学基金，教育部优秀年轻教师基金和回国人员基金，四川省学术和技术带头人培养基金等多项基金。现任中国数学会普委会副主任，中国核学会计算物理学会理事，成都市应用数学会秘书长，教育部回国人员科研启动基金评审专家。多次到境外进行学术访问。2003年入选四川省学术与技术带头人后备人选。

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2009-04-27

【期刊论文】GLOBAL EXISTENCE AND BLOW-UP TO A REACTION-DIFFUSION SYSTEM WITH NONLINEAR MEMORY

穆春来， LILI Du a， CHUNLAI Mu b， ZHAOYIN Xiang b， c

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS Volume 4, Number 4, December 2005 pp. 721-733，-0001，（）：

-1年11月30日

摘要

In this paper, we consider a reaction-diffusion system coupled by nonlinear memory. Under appropriate hypotheses, we prove that the solution either exists globally or blows up in finite time. Furthermore, the blow-up rate estimates are obtained.

Global existence， blow-up， reaction-diffusion system， nonlinear memory

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2009-04-27

【期刊论文】BLOW-UP AND GLOBAL EXISTENCE FOR A COUPLED SYSTEM OF DEGENERATE PARABOLIC EQUATIONS IN A BOUNDED DOMAIN*

穆春来， Mu Chunlai， Hu Xuegang， Li Yuhuan， Cui Zejian

Acta Mathematica Scientia 2007, 27B (1): 92-106，-0001，（）：

-1年11月30日

摘要

This article deals with the conditions that ensure the blow-up phenomenon or its absence for solutions of the system ut=△ul+uPlvql and vt=△vm+uP2vq2 with homogeneous Dirichlet boundary conditions. The results depend crucially on the sign of the difference p2ql-(l-pl)(m-q2), the initial data, and the domain Ω.

Global existence， blow-up， degenerate parabolic system

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2009-04-27

【期刊论文】Neumann problem for reaction-diffusion systems with nonlocal nonlinear sources ☆

穆春来， Zhaoyin Xiang a， b， ∗， Xuegang Hu a， c， Chunlai Mu a

Nonlinear Analysis 61(2005)1209-1224，-0001，（）：

-1年11月30日

摘要

This paper considers the Neumann problem for several types of systems with nonlocal nonlinear terms. We first give the blow-up conditions. And then, for the blow-up solution, we establish the precise blow-up estimates and show the blow-up set is the whole region.

Diffusion system， Nonlocal source， Global existence and blowup， Blow-up estimates

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2009-04-27

【期刊论文】Life span and a new critical exponent for a degenerate parabolic equation

穆春来， Yuhuan Li， Chunlai Mu∗

J. Differential Equations 207(2004)392-406，-0001，（）：

-1年11月30日

摘要

In this paper, we consider the positive solution of the Cauchy problem for the equation ut=up△u+uq, p>1,q>1 and give a secondary critical exponent of the behavior of initial value at infinity for the existence of global and nonglobal solutions of the Cauchy problem. Furthermore, the life span of solutions are also studied.

Blow-up， Life span， Global existence， Critical exponent， Degenerate parabolic equation， Slowly decaying initial data， Self-solution

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2009-04-27

【期刊论文】Output Regulation of Nonlinear Singularly Perturbed Systems

穆春来， JIMIN Yu， CHUNLAI Mu*， XIAOWU Mu AND SHUWEI CHEN

，-0001，（）：

-1年11月30日

摘要

In this paper, the state feedback regulator problem of nonlinear singularly perturbed systems is discussed. It is shown that, under standard assumptions, this problem is solvable if and only if a certain nonlinear partial differential equation is solvable. Once this equation is solvable, a feedback law which solves the problem can easily be constructed. The developed control law is applied to a nonlinear chemical process.

output regulation， Singular perturbations， State feedback， Poisson stability， Chemical process

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2009-04-27

【期刊论文】The Blow-Up Rate for a Strongly Coupled System of Semilinear Heat Equations with Nonlinear Boundary Conditions

穆春来， Chunlai Mu and Shaoyong Lai

Journal of Mathematical Analysis and Applications 254, 524-537 (2001)，-0001，（）：

-1年11月30日

摘要

The paper deals with the blow-up rate of positive solutions to the system u1=uxx+ul11 Vl12, Vl=Vxx+ul21Vl22 with boundary conditions Ux(1, t)=(Up11Up12) (1, t) and Ux(1, t)=(Up21Up22)(1,t). Under some assumptions on the matrices L=(Lij) and P=(pij) and on the initial data u0, v0, the solution (u,v) blows up at finite time T, and we prove that max X∈[0,1] V(x,t) goes to infinity as (T-t)a1/2 (resp. (T-t)a2/2 where ai＜0 are the solutions of (P-Id)(a1,a2)t=(-1,-1)t.