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Controlled Fuzzy Evolution Equations

  • Said MellianiEmail author
  • A. El Allaoui
  • L. S. Chadli
Chapter
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 372)

Abstract

This paper is concerned with controlled fuzzy nonlinear evolution equations of the form
$$\begin{aligned} u'(t) = A\,u(t) + f\Big ( t,u(t),u(\rho (t)) \Big )+B(t)c(t),\quad t\in [t_0,t_1] ; \quad u(t_0) = u_{0}. \end{aligned}$$
Where \(c(t)\in E^1\) is a control, A generate a fuzzy semigroup and \(B:[t_0,t_1]\longrightarrow \mathscr {L}(E^1)\). We use the fuzzy strongly continuous semigroups theory to prove the existence, uniqueness and some properties of mild solutions.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Sultan Moulay Slimane UniversityBeni MellalMorocco

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