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Your search keyword '"Chen, Guowang"' showing total 10 results
Start Over Author "Chen, Guowang" Topic mathematical analysis
10 results on '"Chen, Guowang"'

1. Periodic boundary value problem and cauchy problem of the generalized cubic double dispersion equation

Author

Chen Guowang and Xue Hongxia

Subjects
Cauchy problem, General Mathematics, Weak solution, Mathematical analysis, Free boundary problem, General Physics and Astronomy, Initial value problem, Cauchy distribution, Cauchy boundary condition, Uniqueness, Boundary value problem, Mathematics
Abstract

In this article, the existence, uniqueness and regularities of the global generalized solution and global classical solution for the periodic boundary value problem and the Cauchy problem of the general cubic double dispersion equation u t t - u x x - a u x x t t + b u x 4 - d u x x t = f ( u ) x x are proved, and the sufficient conditions of blow-up of the solutions for the Cauchy problems in finite time are given.

Published
2008

2. Existence and non-existence of global solutions for a class of non-linear wave equations

Author

Yang Zhijian and Chen Guowang

Subjects
Class (set theory), Partial differential equation, General Mathematics, Mathematical analysis, General Engineering, Boundary value problem, Non linear wave, Finite time, Wave equation, Mathematics
Abstract

This paper studies the existence and the non-existence of global solutions to the initial boundary value problems for the non-linear wave equation utt + uxxxx = σ(ux)x + f(x, t) and the Boussinesq-type equation utt + uxxxx = σ(u)xx + f(x, t). The paper proves that every above-mentioned problem has a unique global solution under rather mild confining conditions, and arrives at some sufficient conditions of blow-up of the solutions in finite time. Finally, a few examples are given. Copyright © 2000 John Wiley & Sons, Ltd.

Published
2000

4. Initial value problem for a class of nonlinear pseudo-hyperbolic equations

Author

Yang Zhijian and Chen Guowang

Subjects
Sobolev space, Nonlinear system, Class (set theory), Pure mathematics, Applied Mathematics, Weak solution, Mathematical analysis, Boundary problem, Mathematics::Analysis of PDEs, Initial value problem, Natural number, Hyperbolic partial differential equation, Mathematics
Abstract

The existence of global weak solutions to the periodic boundary problem or the initial value problem for the nonlinear Pseudo-hyperbolic equation $$u_{tt} - \left[ {a_1 + a_2 \left( {u_x } \right)^{2m} } \right]u_{xx} - a_3 u_{xxt} = f\left( {x,t,u,u_x } \right)$$ is proved by the method of the vanishing of the additional diffusion terms, Leray-Schauder's fixed-point argument and Sobolev's estimates, wherem≥1 is a natural number andai>0 (i=1, 2, 3) are constants.

Published
1993

5. Global existence of solution of Cauchy problem for a non-linear wave equation.

Author

Chen, Guowang and Han, Xianjun

Subjects
*CAUCHY problem, *WAVE equation, *WAVE forces, *LINEAR equations, *MATHEMATICAL analysis
Abstract

In this paper, we prove that the Cauchy problem for a non-linear wave equation (1)has a unique global generalized solutions in and a unique global classical solution in . We also prove that the Cauchy problem for the equation (1) admits a unique global generalized solution in C2([0, ∞); Wm, p(R) ∩ L∞(R))(m ≥ 0 is an integer,1 ≤ p ≤ ∞) and a unique global classical solution in . [ABSTRACT FROM AUTHOR]

Published
2013
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6. Cauchy problem for a damped generalized IMBq equation.

Author

Chen, Guowang, Rui, Weifang, and Chen, Xiangying

Subjects
*CAUCHY problem, *DAMPING (Mechanics), *GLOBAL analysis (Mathematics), *NUMERICAL solutions to partial differential equations, *MATHEMATICAL analysis, *MATHEMATICAL physics
Abstract

In this paper, we prove that the Cauchy problem for the following damped generalized IMBq equation, utt-uxx-uxxtt+ν2uxxt=f(u)xx,x∈R,t>0, admits a unique global generalized solution in C3([0,∞);Wm,p(R)∩L∞(R)∩L2(R))(1≤p≤∞,m≥0) and a unique global classical solution in C3([0,∞);Wm,p(R)∩L∞(R)∩L2(R))(m>2+1p). Moreover, the blow up of the solution for the Cauchy problem of damped generalized IMBq equation is studied. We also prove that the Cauchy problem of the above-mentioned equation has a unique global generalized solution in C2([0,∞);Hs(R))(s>12) and a unique global classical solution in C2([0,∞);Hs(R))(s>52), and discuss the blow up of the solution. [ABSTRACT FROM AUTHOR]

Published
2011
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7. Blow-up of solution of Cauchy problem for three-dimensional damped nonlinear hyperbolic equation

Author

Chen, Guowang and Da, Fang

Subjects
*BLOWING up (Algebraic geometry), *CAUCHY problem, *NUMERICAL solutions to hyperbolic differential equations, *NUMERICAL solutions to nonlinear differential equations, *NONLINEAR statistical models, *MATHEMATICAL analysis
Abstract

Abstract: The existence and uniqueness of the local generalized solution and the local classical solution to the Cauchy problem for three-dimensional damped nonlinear hyperbolic equation are proved. This paper arrives at some sufficient conditions for blow-up of the solution in finite time and an example. [Copyright &y& Elsevier]

Published
2009
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8. The initial–boundary value problems for a class of nonlinear wave equations with damping term

Author

Chen, Guowang and Lu, Bo

Subjects
*BOUNDARY value problems, *INITIAL value problems, *WAVE equation, *DAMPING (Mechanics), *BLOWING up (Algebraic geometry), *MATHEMATICAL analysis
Abstract

Abstract: In this paper we study the existence and uniqueness of the global generalized solution and the global classical solution, the blowup of the solution and the energy decay of the solutions of the initial–boundary value problems for a class of nonlinear wave equations. [Copyright &y& Elsevier]

Published
2009
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9. A note on “On the existence of solutions of quasilinear wave equations with viscosity”

Author

Chen, Guowang and Wang, Yanping

Subjects
*DIFFERENTIAL equations, *MATHEMATICAL analysis, *NONLINEAR statistical models, *MATHEMATICAL models
Abstract

Abstract: In the note, we study the existence and uniqueness of the global generalized solution for the following initial boundary value problem: where is a bounded domain in with smooth boundary denotes the Laplacian operator in , denotes the gradient operator and is a given nonlinear function. [Copyright &y& Elsevier]

Published
2008
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10. Cauchy problem of the generalized double dispersion equation

Author

Wang, Shubin and Chen, Guowang

Subjects
*CAUCHY problem, *PARTIAL differential equations, *MATHEMATICAL optimization, *MATHEMATICAL analysis
Abstract

Abstract: In this paper, the existence and the uniqueness of the global solution for the Cauchy problem of the generalized double dispersion equation are proved. The blow-up of the solution for the Cauchy problem of the generalized double dispersion equation is discussed by the concavity method under some conditions. [Copyright &y& Elsevier]

Published
2006
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