外力密度依赖于速度的两类高阶n维非线性发展方程解的爆破  

Blow-up of Solution to Two Classes of Higher-order n-dimensional Nonlinear Evolution Equations with Speed-dependent External Force Densities

作　　者：肖黎明 罗操 XIAO Li-ming;LUO Cao(School of Mathematics and Systems Science,Guangdong Polytechnic Normal University,Guangzhou Guangdong 510665;Teaching Department of Mathematics and Physics,Guangzhou Institute of Science and Technology,Guangzhou Guangdong 510540)

机构地区：[1]广东技术师范大学数学与系统科学学院,广东广州510665 [2]广州理工学院数理教学部,广东广州510540

出　　处：《广东技术师范大学学报》2023年第3期24-28,共5页Journal of Guangdong Polytechnic Normal University

基　　金：广东省教育厅2018年教学团队项目(99161010120);广东省自然科学基金(2018A030313546).

摘　　要：基于两类外力密度依赖于速度的高阶n维非线性发展方程解的爆破问题,研究外力密度依赖于速度的一类在粘弹性力学中具有实际背景的4M阶n维非线性发展方程解的爆破性质,在某些条件下用能量积分结合Jensen不等式研究该类方程解的爆破性质;用能量积分结合Jensen不等式研究外力密度依赖于速度的一类4M+1阶n维非线性发展方程解的爆破性质.This paper studies the blow-up of solution to two classes of higher-order n-dimensional nonlinear evolution equations with speed-dependent external force densities.The first part analyzes the blow-up of solution to a class of 4M-order n-dimensional nonlinear evolution equation with speed-dependent external force density and practical background in viscoelastical mechanics.In the second part,energy integral and Jensen inequality are combined to analyze the blow-up of solution to a class of 4M+1-order n-dimensional nonlinear evolution equation with speed-dependent external force density.

关 键 词：外力密度依赖于速度 高阶非线性发展方程 解的爆破 

分 类 号：O175.2[理学—数学]