Fractional powers approach of operators for abstract evolution equations of third order in time

In this paper we consider approximations of a class of third order linear evolution equations in time governed by fractional powers. We explicitly calculate the fractional powers of matricial operators associated with evolution equations of third order in time, and we characterize the partial scale...

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Bibliographic Details
Published in:Journal of Differential Equations 2020-09, Vol.269 (7), p.5661-5679
Main Authors: Bezerra, Flank D.M., Santos, Lucas A.
Format: Article
Language:English
Subjects:
Approximations
Fractional powers
Sectorial operator
Semigroups
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Summary:In this paper we consider approximations of a class of third order linear evolution equations in time governed by fractional powers. We explicitly calculate the fractional powers of matricial operators associated with evolution equations of third order in time, and we characterize the partial scale of the fractional power of order spaces associated with these operators. As an application, we present parabolic approximations of the Moore-Gibson-Thompson type equations.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2020.04.020