'Wave type' spectrum of the Gurtin-Pipkin equation of the second order
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2010
- DOI:
- 10.48550/arXiv.1002.2831
- arXiv:
- arXiv:1002.2831
- Bibcode:
- 2010arXiv1002.2831I
- Keywords:
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- Mathematics - Complex Variables;
- Mathematical Physics
- E-Print:
- Two typos are corrected