二阶Gurtin-Pipkin方程的“波型”谱
'Wave type' spectrum of the Gurtin-Pipkin equation of the second order
摘要：
研究了二阶Gurtin-Pipkin积分-微分方程在时间上的谱的复部分.我们考虑模型的情况下，当内核是一个指数之和$a_k\exp(-b_k)$与$a_k=1/k^\a$，$b_k=k^\b$。我们证明，有两个复杂的序列的谱点渐近接近的波动方程的谱点。
英文摘要：
We study the complex part of the spectrum of the the Gurtin-Pipkin integral-differential equation of the second order in time. We consider the model case when the kernel is a sum of exponentials $a_k\exp(-b_k)$ with $a_k=1/k^\a$, $b_k=k^\b$. We show that there are two complex sequences of points of the spectrum asymptotically close to the spectrum points of the wave equation.
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