Existence of Global Mild Solutions for Nonautonomous Abstract Evolution Equations

Mian Zhou, Yong Liang and Yong Zhou ()
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Mian Zhou: Faculty of Innovation Engineering, Macau University of Science and Technology, Macau 999078, China
Yong Liang: Faculty of Innovation Engineering, Macau University of Science and Technology, Macau 999078, China
Yong Zhou: Faculty of Innovation Engineering, Macau University of Science and Technology, Macau 999078, China

Mathematics, 2025, vol. 13, issue 11, 1-10

Abstract: In this paper, we investigate the Cauchy problem for nonautonomous abstract evolution equations of the form y ′ ( t ) = A ( t ) y ( t ) + f ( t , y ( t ) ) , t ≥ 0 , y ( 0 ) = y 0 . We obtain new existence theorems for global mild solutions under both compact and noncompact evolution families U ( t , s ) . Our key method relies on the generalized Ascoli–Arzela theorem we previously obtained. Finally, an example is provided to illustrate the applicability of our results.

Keywords: nonautonomous evolution equation; global mild solutions; existence; fixed-point theorem; measure of noncompactness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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