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Existence of Global Mild Solutions for Nonautonomous Abstract Evolution Equations

Author

Listed:
  • 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)

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.

Suggested Citation

  • Mian Zhou & Yong Liang & Yong Zhou, 2025. "Existence of Global Mild Solutions for Nonautonomous Abstract Evolution Equations," Mathematics, MDPI, vol. 13(11), pages 1-10, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1722-:d:1663016
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