Chunlai Mu

ON THE BOUNDNESS OF SOME SOLUTIONS OF THE LÜ SYSTEM

By constructing a suitable Lyapunov function, we show that for the Lu chaotic system parameters in some specified regions, the solutions of the system are globally bounded.

Sixteenth-order method for nonlinear equations

Modification of Newtons method with higher-order convergence is presented. The modification of Newtons method is based on Kings fourth-order method. The new method requires three-step per iteration. Analysis of convergence demonstrates that the order of convergence is 16. Some numerical examples illustrate that the algorithm is more efficient and performs better than classical Newtons method and other methods.

Blow-up and scattering of solution for a generalized Boussinesq equation☆

In this paper, we consider the Cauchy problem for a class of Boussinesq equation. We obtain the existence and uniqueness of the local solutions. For a class of nonlinearity of the perturbation, blow-up solutions are obtained. Furthermore, the global existence and nonlinear scattering for small amplitude solutions are established.

Fifth-order iterative method for finding multiple roots of nonlinear equations

This paper presents a fifth-order iterative method as a new modification of Newton’s method for finding multiple roots of nonlinear equations with unknown multiplicity m. Its convergence order is analyzed and proved. Moreover, several numerical examples demonstrate that the proposed iterative method is superior to the existing methods.

Critical curves for degenerate parabolic equations coupled via non-linear boundary flux

This paper deals with the critical curve for a degenerate parabolic system coupled via non-linear boundary flux. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence curve. The critical curve of Fujita type is conjectured with the aid of some new results. The possible further extensions are also presented.

Blow-up for the ω-heat equation with Dirichlet boundary conditions and a reaction term on graphs

In this paper, we consider the blow-up phenomenon for the -heat equation on graph with Dirichlet boundary conditions and a reaction termwhere is called the discrete weighted Laplacian operators. If , every solution is global, and if and under some suitable conditions, we prove that the nonnegative and nontrivial solution blows up in finite time and the blow-up rate on -norm only depends on p. Finally, two examples are proposed to demonstrate our results.

Global existence and blow-up for degenerate and singular parabolic system with localized sources

This paper deals with the blow-up properties of the solution to degenerate and singular parabolic system with localized sources and homogeneous Dirichlet boundary conditions. The existence of a unique classical nonnegative solution is established and the sufficient conditions for the solution exists globally and blows up in finite time are obtained. Furthermore, under certain conditions, it is proved that the blow-up set of the solution is the whole domain.

Extinction and Positivity of the Solutions for a -Laplacian Equation with Absorption on Graphs

We deal with the extinction of the solutions of the initial-boundary value problem of the discrete p-Laplacian equation with absorption 𝑢𝑡=Δ𝑝,𝜔𝑢−𝑢𝑞 with p > 1, q > 0, which is said to be the discrete p-Laplacian equation on weighted graphs. For 0 < q < 1, we show that the nontrivial solution becomes extinction in finite time while it remains strictly positive for 𝑝≥2, 𝑞≥1 and 𝑞≥𝑝−1. Finally, a numerical experiment on a simple graph with standard weight is given.

Global existence and blow-up to a degenerate reaction–diffusion system with nonlinear memory

In this paper, we consider a degenerate 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 rates are obtained. 2007 Elsevier Ltd. All rights reserved. MSC: 35B33; 35B40; 35K57; 35K60

Boundedness in the higher dimensional attractionrepulsion chemotaxis-growth system

This paper deals with an attractionrepulsion chemotaxis system with logistic source {ut=u(uv)+(uw)+f(u),(x,t)(0,),vt=v1v+1u,(x,t)(0,),wt=w2w+2u,(x,t)(0,), under homogeneous Neumann boundary conditions in a smooth bounded domain Rn(n3) with nonnegative initial data (u0,v0,w0)W1,()W2,()W2,(), where >0, >0, i>0, i>0(i=1,2) and f(u)auu2 with a0 and >0. Based on the maximal Sobolev regularity and semigroup technique, it is proved that the system admits a unique globally bounded classical solution provided that n3, 1=2 and there exists 0>0 such that 1+2<0. The main aim of this paper is to solve the higher-dimensional boundedness question addressed by Xie and Xiang in [IMA J. Appl. Math. 81 (2016) 165198].