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

Non-autonomous impulsive Cauchy problems of parabolic type involving nonlocal initial conditions. (English) Zbl 1295.65061

J. Integral Equations Appl. 26, No. 2, 275-299 (2014).
Summary: We consider a nonautonomous impulsive Cauchy 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.

Cited in 11 Documents

MSC:

65J08 Numerical solutions to abstract evolution equations
35K90 Abstract parabolic equations
35R12 Impulsive partial differential equations

Keywords:

non-autonomous evolution equation; nonlocal initial condition; impulsive condition; parabolicity condition; neutral type; mild solution; Cauchy problem; Banach space
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Full Text: DOI Euclid

References:

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