Electron. J. Diff. Equ., Vol. 2014 (2014), No. 18, pp. 1-9.

Existence and uniqueness of strong solutions for nonlocal evolution equations

Pengyu Chen, Yongxiang Li

Abstract:
The aim of this article is to study the existence and uniqueness of strong solutions for a class of semilinear evolution equations with nonlocal initial conditions. The discussions are based on analytic semigroup theory and fixed point theorems. An example illustrates the main results.

Submitted April 28, 2013. Published January 10, 2014.
Math Subject Classifications: 34G20, 34K30, 35D35, 47D06.
Key Words: Evolution equation; nonlocal initial condition; strong solution; analytic semigroups; existence and uniqueness.

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Pengyu Chen
Department of Mathematics
Northwest Normal University
Lanzhou 730000, China
email: chpengyu123@163.com
Yongxiang Li
Department of Mathematics
Northwest Normal University
Lanzhou 730000, China
email: liyx@nwnu.edu.cn

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