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Forum Mathematicum

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Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


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Volume 31, Issue 1

Issues

Regularity properties of Schrödinger equations in vector-valued spaces and applications

Veli Shakhmurov
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  • Department of Mechanical Engineering, Okan University, Akfirat, Tuzla 34959, Istanbul, Turkey
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Published Online: 2018-09-10 | DOI: https://doi.org/10.1515/forum-2018-0083

Abstract

In this paper, regularity properties and Strichartz type estimates for solutions of the Cauchy problem for linear and nonlinear abstract Schrödinger equations in vector-valued function spaces are obtained. The equation includes a linear operator A defined in a Banach space E, in which by choosing E and A, we can obtain numerous classes of initial value problems for Schrödinger equations, which occur in a wide variety of physical systems.

Keywords: Schrödinger equations; positive operators; semigroups of operators; local solutions

MSC 2010: 35Q41; 35K15; 47B25; 47Dxx; 46E40

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About the article


Received: 2018-04-13

Published Online: 2018-09-10

Published in Print: 2019-01-01


Citation Information: Forum Mathematicum, Volume 31, Issue 1, Pages 149–166, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2018-0083.

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