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2009年04月27日

【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

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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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】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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