Results of a Korteweg-de Vries Equation Generated by a Semigroup of Linear Operators

Abstract

E Aribike, A Y Akinyele, F J Fawehinmi and J O Olabode

In this study, partial contraction mapping with ω-order preservation (ω-OCPn,) is shown to provide a broad class of semilinear initial value issues. By starting with certain conclusions pertaining to such fractional powers, we investigated the application of fractional powers of unbounded linear opera- tors. The fractional powers of A for 0 < α ≤ 1 are defined on the assumption that A is the infinitesimal generator of an analytic semigroup in a Banach space X, 0 ∈ ρ(A). We demonstrated that the closed linear operator Aα with domain D(Aα ) ⊃ D(A) is dense in X. Finally, we determined that the operator is Holder continuous, continuous, and bounded.

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