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Existence and regularity of mild solutions in some interpolation spaces for functional partial differential equations with nonlocal initial conditions

Existence and regularity of mild solutions in some interpolation spaces for functional partial... AbstractThis paper is devoted to study the existence and regularity of mild solutions in some interpolation spaces for a class of functional partial differential equations with nonlocal initial conditions. The linear part is assumed to be a sectorial operator in Banach space X. The fractional power theory and α-norm are used to discuss the problem so that the obtained results can be applied to equations with terms involving spatial derivatives. Moreover, we present an example to illustrate the application of main results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Open Mathematics de Gruyter

Existence and regularity of mild solutions in some interpolation spaces for functional partial differential equations with nonlocal initial conditions

Open Mathematics , Volume 16 (1): 14 – Feb 23, 2018

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Publisher
de Gruyter
Copyright
© 2018 Zhang et al., published by De Gruyter
ISSN
2391-5455
eISSN
2391-5455
DOI
10.1515/math-2018-0012
Publisher site
See Article on Publisher Site

Abstract

AbstractThis paper is devoted to study the existence and regularity of mild solutions in some interpolation spaces for a class of functional partial differential equations with nonlocal initial conditions. The linear part is assumed to be a sectorial operator in Banach space X. The fractional power theory and α-norm are used to discuss the problem so that the obtained results can be applied to equations with terms involving spatial derivatives. Moreover, we present an example to illustrate the application of main results.

Journal

Open Mathematicsde Gruyter

Published: Feb 23, 2018

Keywords: Functional partial differential equation; Nonlocal condition; Strong solution; Analytic compact semigroup; Fractional power operator; α -norm; 34G20; 34K30; 35D35

References