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arXiv · 2107.04148

Fractional powers approach of operators for higher order abstract Cauchy problems

Flank D. M. Bezerra·Lucas A. Santos
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Abstract

In this paper we explore the theory of fractional powers of non-negative (and not necessarily self-adjoint) operators and its amazing relationship with the Chebyshev polynomials of the second kind to obtain results of existence, regularity and behavior asymptotic of solutions for linear abstract evolution equations of $n$-th order in time, where $n\geqslant3$. We also prove generalizations of classical results on structural damping for linear systems of differential equations.

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Flank D. M. Bezerra, Lucas A. Santos. 2021-07-08. Fractional powers approach of operators for higher order abstract Cauchy problems. https://arxiv.org/abs/2107.04148

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