Regularity for evolution equations with nonlocal initial conditions

Regularity for evolution equations with nonlocal initial conditions 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Springer Journals

Regularity for evolution equations with nonlocal initial conditions

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Publisher
Springer Milan
Copyright
Copyright © 2017 by Springer-Verlag Italia
Subject
Mathematics; Mathematics, general; Applications of Mathematics; Theoretical, Mathematical and Computational Physics
ISSN
1578-7303
eISSN
1579-1505
D.O.I.
10.1007/s13398-017-0395-6
Publisher site
See Article on Publisher Site

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.

Journal

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. MatemáticasSpringer Journals

Published: Apr 6, 2017

References

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