带狄利克雷边界条件的小初值耗散半线性波动方程外问题解的破裂及生命跨度估计  

Blow-up and Lifespan Estimate for Semilinear Damped Wave Equation in Exterior Domain with Dirichlet Boundary Condition

作　　者：徐根海[1] 吴邦[2] XU Genhai;WU Bang(Faculty of Engineering,Lishui University,Lishui 323000,Zhejiang;College of Science,Zhejiang Sci-tec University,Hangzhou 310018,Zhejiang)

机构地区：[1]丽水学院工学院,浙江丽水323000 [2]浙江理工大学理学院,浙江杭州310018

出　　处：《丽水学院学报》2018年第2期1-9,共9页Journal of Lishui University

摘　　要：研究在高维外区域上带狄利克雷边界条件的耗散半线性波动方程utt-Δu+ut=|u|p的初边值问题。证明了无论初值多么小,当1<p<1+2/n(n≥3)时,解会在有限时间内破裂;且当1<p<1+2/n时,得到了解的生命跨度上界估计。证明过程中运用了试探函数法。We study the initial boundary value problem of the semilinear damped wave equation in exterior domain in high dimensions.We prove that the solution will blow up in a finite time for 1<p<1+2/n(n≥3),no matter how small the initial data are.What is more,we establish the lifespan estimate from above for 1<p<1+2/n.The test function method is used.

关 键 词：半线性波动方程 破裂 外问题 耗散 狄利克雷边界条件 

分 类 号：O175[理学—数学]