非线性边界条件下拟线性瞬态方程组的Phragmén-Lindel?f型二择一结果  

Phragmén-Lindel?f type alternative results for quasilinear transient equations with nonlinear boundary conditions

作　　者：李远飞 肖胜中[2] 曾鹏 欧阳柏平 LI Yuanfei;XIAO Shengzhong;ZENG Peng;OUYANG Baiping(Guangzhou Huashang College,Guangzhou 511300,China;Guangdong AIB College,Guangzhou 510507,China)

机构地区：[1]广州华商学院,广东广州511300 [2]广东农工商职业技术学院,广东广州510507

出　　处：《浙江大学学报（理学版）》2022年第6期662-669,共8页Journal of Zhejiang University（Science Edition）

基　　金：广东省普通高校创新团队项目(2020WCXTD008)。

摘　　要：考虑了一类定义在三维半无穷柱体上的拟线性方程组,其中假设方程的解在柱体的有限端和侧面满足非齐次条件。定义了“能量”表达式,通过限制非线性项,利用微分不等式技术,推导了一阶微分不等式,解此不等式得到二择一结果,即证明了“能量”随与有限端距离的增大要么呈指数式(多项式)增加,要么呈指数式(多项式)衰减。同时,在衰减情形下得到了全能量的上界。In this paper, we consider a class of quasilinear equations defined on a three-dimensional semi-infinite cylinder, in which the solutions of the equations are assumed to satisfy the nonhomogeneous conditions on both the finite end and the side of the cylinder. An expression of "energy" is defined. By limiting the nonlinear terms and making full use of the differential inequality technique, we obtain a first order differential inequality. By solving this inequality,we prove the alternative results, i. e., the "energy" increases exponentially(polynomial) or decays exponentially(polynomial) with the distance from the finite end. Finally, in the case of decay, we get the upper bound of total energy.

关 键 词：拟线性方程 非线性边界条件 Phragmen-Lindelof型二择一 空间衰减性 

分 类 号：O175.29[理学—数学]