On the blow up time estimation to the Schrödinger equation
There is considered the Schrödinger equation ∂u/∂t= i Δu+ i|u|p , u, t > 0, with initial condition u(0, x)= u0(x), x ∈ Rn, n = 1. We prove the existence of the u0(x) such, that the blow up time estimation increases if p increases in the intervale 4 < p < p0.
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2023-11-01
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| Series: | Lietuvos Matematikos Rinkinys |
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| Online Access: | https://www.journals.vu.lt/LMR/article/view/24559 |
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| _version_ | 1832593226077306880 |
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| author | Gintaras Puriuškis |
| author_facet | Gintaras Puriuškis |
| author_sort | Gintaras Puriuškis |
| collection | DOAJ |
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There is considered the Schrödinger equation ∂u/∂t= i Δu+ i|u|p , u, t > 0, with initial condition u(0, x)= u0(x), x ∈ Rn, n = 1. We prove the existence of the u0(x) such, that the blow up time estimation increases if p increases in the intervale 4 < p < p0.
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| format | Article |
| id | doaj-art-d7cce8b10472420e9c7c88d1582ab40a |
| institution | Kabale University |
| issn | 0132-2818 2335-898X |
| language | English |
| publishDate | 2023-11-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj-art-d7cce8b10472420e9c7c88d1582ab40a2025-01-20T18:15:06ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2023-11-0145spec.10.15388/LMR.2005.24559On the blow up time estimation to the Schrödinger equationGintaras Puriuškis0Vilnius University There is considered the Schrödinger equation ∂u/∂t= i Δu+ i|u|p , u, t > 0, with initial condition u(0, x)= u0(x), x ∈ Rn, n = 1. We prove the existence of the u0(x) such, that the blow up time estimation increases if p increases in the intervale 4 < p < p0. https://www.journals.vu.lt/LMR/article/view/24559nonlinear problemcritical powerglobal solutionblow upShrodinger equation |
| spellingShingle | Gintaras Puriuškis On the blow up time estimation to the Schrödinger equation Lietuvos Matematikos Rinkinys nonlinear problem critical power global solution blow up Shrodinger equation |
| title | On the blow up time estimation to the Schrödinger equation |
| title_full | On the blow up time estimation to the Schrödinger equation |
| title_fullStr | On the blow up time estimation to the Schrödinger equation |
| title_full_unstemmed | On the blow up time estimation to the Schrödinger equation |
| title_short | On the blow up time estimation to the Schrödinger equation |
| title_sort | on the blow up time estimation to the schrodinger equation |
| topic | nonlinear problem critical power global solution blow up Shrodinger equation |
| url | https://www.journals.vu.lt/LMR/article/view/24559 |
| work_keys_str_mv | AT gintaraspuriuskis ontheblowuptimeestimationtotheschrodingerequation |