Marcelo J. D. Nascimento, Flank D. M. Bezerra
In this article we study non-autonomous approximations governed by the fractional powers of damped wave operators of order subject to Dirichlet boundary conditions in an -dimensional bounded domain with smooth boundary. We give explicitly expressions for the fractional powers of the wave operator, we compute their resolvent operators and their eigenvalues. Moreover, we study the convergence as with rate .
Submitted January 24, 2019. Published May 17, 2019.
Math Subject Classifications: 35L05, 35B40.
Key Words: Non-autonomous damped wave equations; fractional powers; rate of convergence; eigenvalues.
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| Marcelo J. D. Nascimento |
Universidade Federal de São
Carlos, Departamento de Matemática
13565-905 São, Carlos SP, Brazil
| Flank D. M. Bezerra |
Departamento de Matemática
Universidade Federal da Paraíba
58051-900 João Pessoa PB, Brazil
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