Geodesic
Stability of parabolic equations with unbounded operators acting on delay terms
Electronic journal of differential equations, Tome 2014 (2014)
In this article, we study the stability of the initial value problem for the delay differential equation

$\displaylines{ \frac{dv(t)}{dt}+Av(t)=B(t)v(t-\omega )+f(t),\quad t\geq 0,\cr v(t)=g(t)\quad (-\omega \leq t\leq 0) }$

in a Banach space E with the unbounded linear operators A and $B(t)$ with dense domains $D(A)\subseteq D(B(t))$. We establish stability estimates for the solution of this problem in fractional spaces $E_{\alpha }$. Also we obtain stability estimates in Holder norms for the solutions of the mixed problems for delay parabolic equations with Neumann condition with respect to space variables.
Classification : 35K30
Keywords: delay parabolic equation, stability estimate, fractional space, holder norm 
@article{EJDE_2014__2014__a149,
     author = {Ashyralyev,  Allaberen and Agirseven,  Deniz},
     title = {Stability of parabolic equations with unbounded operators acting on delay terms},
     journal = {Electronic journal of differential equations},
     year = {2014},
     volume = {2014},
     zbl = {1297.35028},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a149/}
}
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AU  - Agirseven,  Deniz
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%U http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a149/
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Ashyralyev,  Allaberen; Agirseven,  Deniz. Stability of parabolic equations with unbounded operators acting on delay terms. Electronic journal of differential equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a149/