L 2 -convergence results for linear dissipative wave equations in unbounded domains
L 2 -convergence results for linear dissipative wave equations in unbounded domains
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L 2 -无界域中线性耗散波方程的收敛结果
作者：
R. Ikehata
首先考虑实希尔伯特空间 H 中具有“非负”自共轭算子 A 的双曲线性柯西问题 eu + Au + u = 0, u(0) = u0, u(0) = u1。结果表明，解 ue 在某种意义上趋向于某个解 v，即 e ↓ 0f 或抛物方程 v + Av = 0。给出了一些应用。最后，我们提出了双曲-双曲收敛结果，例如当阻尼效应在具体环境中消失时，阻尼波动方程的解会变成自由波动方程的某个解。
Hyperbolic linear Cauchy problem eu + Au + u = 0, u(0) = u0, u(0) = u1, with "nonnegative" selfadjoint operator A in a real Hilbert space H is first considered. It is shown that the solution ue tends to some solution v as e ↓ 0f or the parabolic equation v + Av = 0 in a certain sense. Some applications are given. Finally, we present hyperbolic-hyperbolic convergence results such as the solution for the damped wave equations goes to some solution for the free wave equations as the effect of the damping vanishes in a concrete context.