一类双曲方程解的空间渐近性态  

Spatial asymptotic behavior of solutions for a class of hyperbolic equations

作　　者：石金诚 SHI Jin-cheng(School of Date Science,Guangzhou Huashang College,Guangzhou 511300,China)

机构地区：[1]广州华商学院数据科学学院,广东广州511300

出　　处：《高校应用数学学报（A辑）》2022年第3期268-276,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：广东省高等学校青年创新人才项目(自然科学)(2021KQNCX134);国家自然科学基金(11371175);广东普通高校重点科研项目(自然科学)(2019KZDXM042);广东省普通高校人文社科类创新团队(2020WCXTD008)。

摘　　要：研究了一类双曲方程的解的空间性态,利用能量方法与微分不等式的技巧得到了解的类似于Phragmen-Lindelof二择一定理的结果:沿空间变量z趋于无穷大时解或者爆破,或者衰减.接着在解衰减的基础上得到解的衰减为指数衰减,最后得到解的点点指数衰减估计.该文的结果可看成Saint-Venant原则在双曲方程上的应用.The spatial behavior of solutions for a class of hyperbolic equations is studied.By using the energy method and the technique of differential inequality,a result similar to the alternative theorem of Phragmen-Lindelof is obtained:when the spatial variable z tends to infinity,the solution either blows up or decays.Then,on the basis of the solution decay,the solution decay is exponential decay is got.Finally,the point exponential decay estimate of the solution is obtained.The results in this paper can be regarded as the application of Saint-Venant principle to hyperbolic equations.

关 键 词：空间性态 双曲方程 Phragmen-Lindelof二择一 爆破 

分 类 号：O175.29[理学—数学]