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Regularity for evolution equations with nonlocal initial conditions

  • Pengyu Chen
  • Xuping Zhang
  • Yongxiang Li
Original Paper
  • 87 Downloads

Abstract

This paper is concerned with the existence and uniqueness of global strong solutions for a class of semilinear evolution equations with nonlocal initial conditions on infinite interval. We assume that the linear part is a positive definite selfadjoint operator, and the nonlinear part satisfies some essential growth conditions. The discussions are based on analytic semigroups theory, the piecewise regular method and relevant fixed point theorem. The results obtained in this paper improve and extend some related conclusions on this topic. An example to illustrate the feasibility of our abstract results is also given.

Keywords

Evolution equations Nonlocal initial condition Compact analytic semigroup Strong solution 

Mathematics Subject Classification

46B50 47H20 47J35 

Notes

Acknowledgements

The authors would like to thank the anonymous referees for their carefully reading the manuscript and very important comments and suggestions that improved the results and quality of this paper. P. Chen acknowledge support from NNSF of China (No. 11501455) and Key Project of Gansu Provincial National Science Foundation (No. 1606RJZA015). Y. Li acknowledge support from NNSF of China (No. 11661071).

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Copyright information

© Springer-Verlag Italia 2017

Authors and Affiliations

  1. 1.Department of MathematicsNorthwest Normal UniversityLanzhouPeople’s Republic of China

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