任意高初始能量下一类耦合非线性发展方程组解的爆破  

Blow-up of Solutions for a Class of Coupled Nonlinear Evolution Equations with Arbitrary High Initial energy

作　　者：阳志锋[1] 

机构地区：[1]衡阳师范学院数学与计算科学系,湖南衡阳421008

出　　处：《应用数学》2014年第3期491-497,共7页Mathematica Applicata

基　　金：湖南省自然科学基金(14JJ7070);湖南省重点建设学科(运筹学与控制论;衡阳师范学院[2011]76)

摘　　要：在Rn上考虑一类具弱阻尼的耦合非线性发展方程组的柯西问题,获得任意高初始能量下弱解的blow-up结果,推广了已有的结论.为了克服Rn上庞加莱不等式缺失的不足,本文先将问题的解分解为线性和非线性两部分,并做相应的傅立叶变换,然后利用有限传播速度性质来对与解相关的某些范数作估计.The Cauchy problem for a coupled evolution equations with nonlinear weakly damping on the whole space Rnis considered.A blow up result of weak solution with arbitrarily positive initial energy is obtained.And it generalized some previous results about this system.To overcome the lack of the Poincare inequality in Rn,the finite speed of propagation property of solutions be used here to estimate some norm in relation to solution,after the solution be decomposed into linear and nonlinear terms,and be performed the Fourier transform.

关 键 词：发展方程 非线性阻尼 柯西问题 解的爆破 

分 类 号：O175.29[理学—数学]