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math.AP2021
Fractional powers approach of operators for higher order abstract Cauchy problems
Flank D. M. Bezerra, Lucas A. Santos
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…
math.AP2021
Well-posedness for some third-order evolution differential equations: A semigroup approach
Flank D. M. Bezerra, Alexandre N. Carvalho, Lucas A. Santos
In this paper, we discuss the well-posedness of the Cauchy problem associated with the third-order evolution equation in time $$ u_{ttt} +A u + ηA^{\frac13} u_{tt} +ηA^{\frac23} u_…