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A. Y. Akinyele, F. J. Fawehinmi, Y. Saka-Balogun and L. K. Alhassan, Results of semigroup of linear equations generating Lipschitz perturbations of linear evolution equations, Eur. J. Math. Appl. 5 (2025), Article ID 13.

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Volume 5 (2025), Article ID 13

https://doi.org/10.28919/ejma.2025.5.13

Published: 07/08/2025

Abstract:

In this paper, results of $\omega$-order preserving partial contraction mapping generating Lipschitz perturbations of linear evolution equation was presented. A certain semilinear value problem was studied where $A$ is the infinitesimal generator of a $C_0$-semigroup $\{T(t),\ t\geqslant 0\}$ on a Banach space $X$ and $f:[t_0,T]\times X\rightarrow X$ is continuous in $t$ and satisfies a Lipschitz condition in $u$. We assume $A$ to be independent of $t$ and was extended to the case where $A$ depends on $t$ in a way that insure the existence of an evolution system $U(t,s)$, $0\leqslant s\leqslant t\leqslant T$, for the family $\{A(t)\}_{t\in[0,T]}$ and shows that the initial value problem have a mild solution.

How to Cite:

A. Y. Akinyele, F. J. Fawehinmi, Y. Saka-Balogun and L. K. Alhassan, Results of semigroup of linear equations generating Lipschitz perturbations of linear evolution equations, Eur. J. Math. Appl. 5 (2025), Article ID 13. https://doi.org/10.28919/ejma.2025.5.13