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Topological theory of non-autonomous parabolic evolution inclusions on a noncompact interval and applications

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Abstract

In this paper we consider the topological structure of the solution set of non-autonomous parabolic evolution inclusions with time delay, defined on non-compact intervals. The result restricted to compact intervals is then extended to non-autonomous parabolic control problems with time delay. Moreover, as the applications of the information about the structure, we establish the existence result of global integral solutions for non-autonomous Cauchy problems subject to nonlocal condition, and prove the invariance of a reachability set for non-autonomous control problems under single-valued nonlinear perturbations. Finally, some illustrating examples are supplied.

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Acknowledgments

The first author acknowledges support from the NNSF of China (Nos. 11471083, 11101202). The second author acknowledges support from the University Scientific and Technological Innovation Project of Guangdong Province (No. 2013KJCX0068). The third author acknowledges support from the NNSF of China (No. 11271309) and the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20114301110001). The authors also want to express their thanks to the anonymous referees for their suggestions and comments that improved the quality of the paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Guangdong University of Foreign Studies, Guangzhou, 510006, Guangdong, People’s Republic of China

    Rong-Nian Wang & Qing-Hua Ma

  2. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, Hunan, People’s Republic of China

    Yong Zhou

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  1. Rong-Nian Wang
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Correspondence to Yong Zhou.

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Wang, RN., Ma, QH. & Zhou, Y. Topological theory of non-autonomous parabolic evolution inclusions on a noncompact interval and applications. Math. Ann. 362, 173–203 (2015). https://doi.org/10.1007/s00208-014-1110-y

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