Journal of Integral Equations and Applications

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

Rong-Nian Wang, Khalil Ezzinbi, and Peng-Xian Zhu

Full-text: Open access

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

Permanent link to this document
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

Subjects
Primary: 65J08: Abstract evolution equations
Secondary: 34A37: Differential equations with impulses 35R12: Impulsive partial differential equations

Keywords
Non-autonomous evolution equation nonlocal initial condition impulsive condition parabolicity condition neutral type mild solution

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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