一类非线性退化双曲方程解的整体存在性和爆破的条件
The Global Existence and Blow-Up Conditions for a Class of Nonlinear Degenerate Hyperbolic Equation
DOI: 10.12677/AAM.2017.64063, PDF, HTML, XML, 下载: 1,765  浏览: 3,133 
作者: 祝佳玲：西南交通大学数学学院，四川 成都
关键词: 退化双曲方程；Galerkin方法；整体解；爆破；Degenerate Hyperbolic Equation； Galerkin Method； Global Solutions； Blow Up
摘要: 本文研究了一类非线性退化双曲方程的初边值问题。借助Galerkin方法得到了解的整体存在性，与此同时，当初始能量为正且有界时，通过分析的方法可以证明解爆破。
Abstract: In this paper, the initial-boundary value problem for a class of degenerate hyperbolic equation is studied. The global existence of solution is obtained by introducing Galerkin method. Also the global nonexistence of solution can be verified by using the analysis method while the initial energy is positive and bounded.
文章引用：祝佳玲. 一类非线性退化双曲方程解的整体存在性和爆破的条件[J]. 应用数学进展, 2017, 6(4): 523-528. https://doi.org/10.12677/AAM.2017.64063

参考文献

[1] John, F. (1979) Blow-Up of Solutions of Nonlinear Wave Equations. Manuscripta Mathematica, 76, 235-268.
https://doi.org/10.1007/BF01647974
[2] Glassey, R. (1981) Finite-Time Blow-Up for Solutions of Nonlinear Wave Equations. Mathematische Zeitschrift, 177, 323-340.
https://doi.org/10.1007/BF01162066
[3] Ye, Y.J. (2005) Existence and Nonexistence of Global Solutions of the Initial-Boundary Value Problem for Some Degenerate Hyperbolic Equation. Journal of Mathematical Physics, 25, 703-709.
[4] 张健. 一个退化双曲方程的初边值问题[J]. 四川师范大学学报, 1993, 16(2): 43-46.
[5] 管楚洤. 非线性退化双曲方程的Cauchy问题[J]. 科学通报, 1982, 1982(23): 1409-1413.
[6] Yang, X.F. (2006) Lower Bounds on Life-Span of Classical Solution to Quasi-Linear Hyperbolic Systems. Journal of Mathematics, 26, 237-242.

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