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| 一类推广的IMBq方程解的爆破 | |
| 引用本文： | 刘洋,赵军生,于涛. 一类推广的IMBq方程解的爆破[J]. 河北大学学报(自然科学版), 2011, 31(3): 240-243 |
| 作者姓名： | 刘洋 赵军生 于涛 |
| 作者单位： | 1. 西北民族大学数学与计算机科学学院,甘肃兰州,730124 2. 黑龙江大学数学科学学院,黑龙江,哈尔滨,150080 3. 哈尔滨工程大学理学院,黑龙江哈尔滨,150001 |
| 基金项目： | 国家自然科学基金资助项目 |
| 摘 要： | 对一类推广的IMBq方程的初边值问题进行了研究,在非线性项满足一定条件的情况下,采用特征函数法和凸性方法,证明了问题的光滑解只能在时间的一个有界区间中存在,并且在有限时间T内爆破,即解于有限时间T内在某种意义下趋于无穷大,从而说明了这类典型的非线性发展方程解的奇性. |
| 关 键 词： | IMBq方程 初边值问题 特征函数法 凸性方法 爆破 |
Blow-up of Solutions for a Class of Generalized IMBq Equations |
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| LIU Yang,ZHAO Jun-sheng,YU Tao. Blow-up of Solutions for a Class of Generalized IMBq Equations[J]. Journal of Hebei University (Natural Science Edition), 2011, 31(3): 240-243 | |
| Authors: | LIU Yang ZHAO Jun-sheng YU Tao |
| Affiliation: | 1.College of Mathematics and Computer Science,Northwest University for Nationalities,Lanzhou 730124,China;2.School of Mathematical Science,Heilongjiang University,Harbin 150080,China;3.College of Science,Harbin Engineering University,Harbin 150001,China) |
| Abstract: | The initial boundary value problem of solutions for a class of generalized IMBq equations is studied.In the case of the nonlinear term satisfying some conditions,it is proved by using the eigenfunction method and convexity method that smooth solutions of the problem only exist in a bounded time interval and blow up in the finite time T,that is,the solutions tend to infinity in the finite time T in a sense.Consequently,the conclusion of this paper indicates the singularity of solutions for this typical nonlinear evolution equations. |
| Keywords: | IMBq equations initial boundary value problem eigenfunction method convexity method blow-up |
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