On the Well-Posedness and Asymptotic Behavior of an Initial-Boundary Value Problem for a Heterogeneous Hot Standby Renewable Reliability System

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DOI: https://doi.org/10.28924/2291-8639-24-2026-332
Published: Oct 5, 2026
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Alim Mijit, On the Well-Posedness and Asymptotic Behavior of an Initial-Boundary Value Problem for a Heterogeneous Hot Standby Renewable Reliability System, Int. J. Anal. Appl., 24 (2026), 332.

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Alim Mijit

Abstract

In this research, we investigated the well-posedness and asymptotic behavior of an initial-boundary value problem (IBVP) associated with a heterogeneous hot-standby renewable reliability system. First, we established the well-posedness of the system model by leveraging \(C_0\)-semigroup theory from functional analysis to ensure the existence and uniqueness of solutions. Second, by analyzing the spectral properties of the operator corresponding to the IBVP, we demonstrated that zero is an eigenvalue for the operator and its adjoint with geometric multiplicity one. Further, we showed that all non-zero points on the imaginary axis lie within the resolvent set of the operator. Based on these findings, we concluded that the time-dependent solution of the IBVP converges strongly to its steady-state solution as time approaches infinity.

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