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2009年04月27日

【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

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年04月27日

【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.

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2009年04月27日

【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年04月27日

【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年04月27日

【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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