Open Access
SUMMER 2014 Non-autonomous impulsive Cauchy problems of parabolic type involving nonlocal initial conditions
Rong-Nian Wang, Khalil Ezzinbi, Peng-Xian Zhu
J. Integral Equations Applications 26(2): 275-299 (SUMMER 2014). DOI: 10.1216/JIE-2014-26-2-275


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.


Download Citation

Rong-Nian Wang. Khalil Ezzinbi. Peng-Xian Zhu. "Non-autonomous impulsive Cauchy problems of parabolic type involving nonlocal initial conditions." J. Integral Equations Applications 26 (2) 275 - 299, SUMMER 2014.


Published: SUMMER 2014
First available in Project Euclid: 21 July 2014

zbMATH: 1295.42004
MathSciNet: MR3233521
Digital Object Identifier: 10.1216/JIE-2014-26-2-275

Primary: 65J08
Secondary: 34A37 , 35R12

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

Rights: Copyright © 2014 Rocky Mountain Mathematics Consortium

Vol.26 • No. 2 • SUMMER 2014
Back to Top