Stability of parabolic equations with unbounded operators acting on delay terms

Ashyralyev A., AĞIRSEVEN D.

Electronic Journal of Differential Equations, vol.2014, 2014 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2014
  • Publication Date: 2014
  • Journal Name: Electronic Journal of Differential Equations
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Delay parabolic equation, Fractional space, Höolder norm, Stability estimate
  • Trakya University Affiliated: Yes

Abstract

In this article, we study the stability of the initial value problem for the delay differential equation in a Banach space E with the unbounded linear operators A and B(t) with dense domains D(A) ⊆ D(B(t)). We establish stability estimates for the solution of this problem in fractional spaces Eα. Also we obtain stability estimates in Höolder norms for the solutions of the mixed problems for delay parabolic equations with Neumann condition with respect to space variables. © 2014 Texas State University - San Marcos.