On a Local Energy Decay of Solutions of a Dissipative Wave Equation(Mathematical Analysis of Phenomena in Fluid and Plasma Dynamics)
On a Local Energy Decay of Solutions of a Dissipative Wave Equation(Mathematical Analysis of Phenomena in Fluid and Plasma Dynamics)
复制标题
关于耗散波方程解的局部能量衰变（流体和等离子体动力学现象的数学分析）
DOI：
10.1016/0022-247x(66)90045-x
复制
发表时间：
1994
影响因子：
1.3
通讯作者：
檀 和日子
中科院分区：
文献类型：
--
作者：
柴田 良弘;檀 和日子
本文讨论了双曲型方程初边值问题解在无界区域上的衰减性问题。这里考虑的方程属于一类二阶线性双曲型偏微分方程的二阶总能量保持常数。假设空间区域的补集是星星形的，并且初始数据具有紧支撑。本文证明了在一定条件下，能量传播到无穷远，特别是包含在任何有限球中的能量像t-（l-al）一样衰减，其中0 <$'pi < 1依赖于系数的径向导数的界. Wilcox [1] Morawetz [2，31，Lax and菲利普斯[4]，Lax，Morawetz，和菲利普斯[5]，和Zachmanoglou [6，71。Lieberman [8]处理了波动方程的相应问题，其中二阶时间导数的系数取决于距原点的径向距离。本文采用的方法是Morawetz和Lieberman方法的推广。
This paper deals with the question of decay of solutions of the initialboundary value problem for hyperbolic equations in unbounded regions. The equations considered here belong to a class of second order linear hyperbolic partial differential equations of the second order for which the total energy remains constant. It is assumed that the complement of the space region is star shaped and that the initial data have compact support. It is shown that under certain conditions the energy travels out to infinity and specifically that the energy contained in any finite sphere decays like t-(l-al) where 0<‘pi< 1 depends on the bounds of the radial derivatives of the coefficients.The corresponding problem for the wave equation has been dealt with by Wilcox [l] Morawetz [2, 31, Lax and Phillips [4], Lax, Morawetz, and Phillips [5], and Zachmanoglou [6, 71. Lieberman [8] dealt with the corresponding problem for the wave equation in which the coefficient of the second order time derivative depends on the radial distance from the origin. The methods employed in this paper are extensions of the methods of Morawetz and Lieberman.