On the Decay of Solutions to a Class of Hartree Equations: On the decay of solutions to a class of Hartree equations
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| Názov: | On the Decay of Solutions to a Class of Hartree Equations: On the decay of solutions to a class of Hartree equations |
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| Autori: | Tarulli, Mirko, Venkov, George |
| Informácie o vydavateľovi: | Bulgarian Academy of Sciences - BAS (Bălgarska Akademiya na Naukite - BAN), Sofia, 2019. |
| Rok vydania: | 2019 |
| Predmety: | Non-linear Schrödinger еquations, nonlinear Schrödinger equations, Morawetz inequalities, NLS equations (nonlinear Schrödinger equations), Scattering theory for PDEs, Hartree equations, Nonlinear differential equations in abstract spaces |
| Popis: | In the paper under consideration nonlinear defocusing Schrödinger equations with Hartree-type nonlinearity is studied. The authors prove that global solution of the Cauchy problem for such equation has peculiar decay property. To do this a combination of a localization trick, the nonlinear interaction Morawetz estimate and interpolation is applied. In this way the long-time behavior of the solutions of the problem under consideration in the space \( L^{q}(\mathbb{R}^{d})\) is obtained which leads to the scattering in the energy space. |
| Druh dokumentu: | Article |
| Popis súboru: | application/xml |
| Prístupová URL adresa: | https://zbmath.org/7159537 https://hdl.handle.net/10525/3624 |
| Prístupové číslo: | edsair.dedup.wf.002..a7c49e4d2976405a7fc9549fbfb3674f |
| Databáza: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | In the paper under consideration nonlinear defocusing Schrödinger equations with Hartree-type nonlinearity is studied. The authors prove that global solution of the Cauchy problem for such equation has peculiar decay property. To do this a combination of a localization trick, the nonlinear interaction Morawetz estimate and interpolation is applied. In this way the long-time behavior of the solutions of the problem under consideration in the space \( L^{q}(\mathbb{R}^{d})\) is obtained which leads to the scattering in the energy space. |
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