## Journal of Integral Equations and Applications

### Non-autonomous impulsive Cauchy problems of parabolic type involving nonlocal initial conditions

#### Abstract

We consider a nonautonomous impulsive Cau\-chy problem of parabolic type involving a nonlocal initial condition in a Banach space $X$, where the operators in linear part (possibly unbounded) depend on time $t$ and generate an evolution family. New existence theorems of mild solutions to such a problem, in the absence of compactness and Lipschitz continuity of the impulsive item and nonlocal item, are established. The non-autonomous impulsive Cauchy problem of neutral type with nonlocal initial condition is also considered. Comparisons with available literature are also given. Finally, as a sample of application, these results are applied to a system of partial differential equations with impulsive condition and nonlocal initial condition. Our results essentially extend some existing results in this area.

#### Article information

Source
J. Integral Equations Applications, Volume 26, Number 2 (2014), 275-299.

Dates
First available in Project Euclid: 21 July 2014

https://projecteuclid.org/euclid.jiea/1405949665

Digital Object Identifier
doi:10.1216/JIE-2014-26-2-275

Mathematical Reviews number (MathSciNet)
MR3233521

Zentralblatt MATH identifier
1295.42004

#### Citation

Wang, Rong-Nian; Ezzinbi, Khalil; Zhu, Peng-Xian. Non-autonomous impulsive Cauchy problems of parabolic type involving nonlocal initial conditions. J. Integral Equations Applications 26 (2014), no. 2, 275--299. doi:10.1216/JIE-2014-26-2-275. https://projecteuclid.org/euclid.jiea/1405949665

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