Diffusion Phenomenon for Linear Dissipative Wave Equations
Diffusion Phenomenon for Linear Dissipative Wave Equations
复制标题
线性耗散波方程的扩散现象
DOI：
10.4171/zaa/1459
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发表时间：
2012
影响因子：
1.2
通讯作者：
B. Said
中科院分区：
文献类型：
--
作者：
B. Said
本文证明了线性波动方程的扩散现象。为了推导扩散现象，采用了一种新的方法。事实上,一些加权空间的初始数据,我们证明2 p≤≤∞,为u−v为Lp (RN)衰变率t−2(1−1 p)−1−γ2γ∈[0,1]的速度比u或v,你在哪里线性波动方程的解与初始数据(情况,u1)∈(H1 (RN)∩L1,γ(RN))×(L2 (RN)∩L1,γ(RN))与γ∈[0,1],和v的解决相关热方程和初始数据v0 =情况+ u1。这一结果改进了H. Yang和A. Milani[牛]的研究结果。科学。数学[j] . 124(2000), 415 - 433]，在初始数据的上述限制下，该论文给出的衰减率可以提高t−γ 2。
In this paper we prove the diffusion phenomenon for the linear wave equation. To derive the diffusion phenomenon, a new method is used. In fact, for initial data in some weighted spaces, we prove that for 2 ≤ p ≤ ∞, ‖u− v‖Lp(RN ) decays with the rate t − 2 (1− 1 p )−1− γ 2 , γ ∈ [0, 1] faster than that of either u or v, where u is the solution of the linear wave equation with initial data (u0, u1) ∈ ( H1(RN ) ∩ L1,γ(RN ) ) × ( L2(RN ) ∩ L1,γ(RN ) ) with γ ∈ [0, 1], and v is the solution of the related heat equation with initial data v0 = u0 + u1. This result improves the result in H. Yang and A. Milani [Bull. Sci. Math. 124 (2000), 415 – 433] in the sense that, under the above restriction on the initial data, the decay rate given in that paper can be improved by t− γ 2 .
影响因子：
0.8
作者：
R. Ikehata;K. Nishihara
通讯作者：
R. Ikehata;K. Nishihara