ORIGINAL ARTICLE
On coupled semilinear evolution systems: Techniques on fractional powers of matrices and applications
Maykel B. Belluzi,
Flank D. M. Bezerra,
Marcelo J. D. Nascimento,
Maykel B. Belluzi
Universidade de São Paulo, ICMC, São Carlos, São Paulo, Brazil
Search for more papers by this authorCorresponding Author
Flank D. M. Bezerra
Departamento de Matemática, Universidade Federal da Paraíba, João Pessoa, Paraíba, Brazil
Correspondence
Flank D. M. Bezerra, Departamento de Matemática, Universidade Federal da Paraíba, 58051-900, João Pessoa PB, Brazil.
Email: [email protected]
Search for more papers by this authorMarcelo J. D. Nascimento
Universidade Federal de São Carlos, Departamento de Matemática, São Carlos, São Paulo, Brazil
Search for more papers by this authorMaykel B. Belluzi,
Flank D. M. Bezerra,
Marcelo J. D. Nascimento,
Maykel B. Belluzi
Universidade de São Paulo, ICMC, São Carlos, São Paulo, Brazil
Search for more papers by this authorCorresponding Author
Flank D. M. Bezerra
Departamento de Matemática, Universidade Federal da Paraíba, João Pessoa, Paraíba, Brazil
Correspondence
Flank D. M. Bezerra, Departamento de Matemática, Universidade Federal da Paraíba, 58051-900, João Pessoa PB, Brazil.
Email: [email protected]
Search for more papers by this authorMarcelo J. D. Nascimento
Universidade Federal de São Carlos, Departamento de Matemática, São Carlos, São Paulo, Brazil
Search for more papers by this authorFirst published: 16 June 2024
Abstract
In this paper, we provide several techniques to explicitly calculate fractional powers of operator matrices
focusing on creating a theory that can be applied to distinct situations. To illustrate the abstract results developed, we consider its application in systems of coupled reaction–diffusion equations and in (strongly damped) wave equations. We also discuss how these techniques can be applied to higher order matrices and we specifically calculate the fractional powers of a operator matrix associated to a weakly coupled system of wave equation. In addition, we deal with the applicability of this analysis with respect to solvability, stabilization, regularity, smooth dynamics, and connection with evolutionary classic equation and its fractional counterpart.
CONFLICT OF INTEREST STATEMENT
The authors declare that they have no conflict of interest.
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