Wave Equations With Several Nonlinear Source Terms

LIU Ya-cheng; XU Run-zhang; YU Tao

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LIU Ya-cheng, XU Run-zhang, YU Tao. Wave Equations With Several Nonlinear Source Terms[J]. Applied Mathematics and Mechanics, 2007, 28(9): 1079-1086.

Citation:

LIU Ya-cheng, XU Run-zhang, YU Tao. Wave Equations With Several Nonlinear Source Terms[J]. Applied Mathematics and Mechanics, 2007, 28(9): 1079-1086.

Citation:

LIU Ya-cheng, XU Run-zhang, YU Tao. Wave Equations With Several Nonlinear Source Terms[J]. Applied Mathematics and Mechanics, 2007, 28(9): 1079-1086.

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Wave Equations With Several Nonlinear Source Terms

College of Science, Harbin Engineering University, Harbin 150001, P. R. China

Received Date: 2006-07-26
Rev Recd Date: 2007-06-28
Publish Date: 2007-09-15

Abstract

Abstract

The initial boundary value problem of nonlinear wave equations with several nonlinear source terms in a bounded domain is studied by potential well method. The structure of potential wells and some properties of depth function of potential well are given. The invariance of some sets under the flow of these problems and the vacuum isolating of solutions are obtained by introducing a family of potential wells, which indicates that if initial value of the problem belongs to potential well or its outside, all the solutions for the problem are in the same potential well or its outside respectively in any time. At the same time, there exists a region, in which there are no any solutions. Then the threshold result of global existence and nonexistence of solutions are given. Finally the problems with critical initial conditions are discussed.
- wave equation,
- potential well,
- global existence,
- nonexistence

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References(15)

References

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