Scattering in the Energy Space for Solutions of the Damped Nonlinear Schrödinger Equation on <inline-formula><math display="inline"><semantics><mrow><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>d</mi></msup><mo>×</mo><mi mathvariant="double-struck">T</mi></mrow></semantics></math></inline-formula>
We will show, in any space dimension <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>≥</mo><mn>3</mn></mrow></semantics></math></inlin...
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2025-06-01
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| author | Taim Saker Mirko Tarulli George Venkov |
| author_facet | Taim Saker Mirko Tarulli George Venkov |
| author_sort | Taim Saker |
| collection | DOAJ |
| description | We will show, in any space dimension <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>≥</mo><mn>3</mn></mrow></semantics></math></inline-formula>, the decay and scattering in the energy space for the solution to the damped nonlinear Schrödinger equation posed on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>d</mi></msup><mo>×</mo><mi mathvariant="double-struck">T</mi></mrow></semantics></math></inline-formula> and initial data in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>H</mi><mn>1</mn></msup><mrow><mo>(</mo><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>d</mi></msup><mo>×</mo><mi mathvariant="double-struck">T</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. We will also derive new bilinear Morawetz identities and corresponding localized Morawetz estimates. |
| format | Article |
| id | doaj-art-967538e6fe4a466d99781a2adfef87f6 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-967538e6fe4a466d99781a2adfef87f62025-08-20T03:32:31ZengMDPI AGAxioms2075-16802025-06-0114644710.3390/axioms14060447Scattering in the Energy Space for Solutions of the Damped Nonlinear Schrödinger Equation on <inline-formula><math display="inline"><semantics><mrow><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>d</mi></msup><mo>×</mo><mi mathvariant="double-struck">T</mi></mrow></semantics></math></inline-formula>Taim Saker0Mirko Tarulli1George Venkov2Institute of Mathematics and Informatics, Bulgarian Academy of Science, Acad. Georgi Bonchev Str., Block 8, 1113 Sofia, BulgariaInstitute of Mathematics and Informatics, Bulgarian Academy of Science, Acad. Georgi Bonchev Str., Block 8, 1113 Sofia, BulgariaDepartment of Mathematical Analysis and Differential Equations, Faculty of Applied Mathematics and Informatics, Technical University of Sofia, 1756 Sofia, BulgariaWe will show, in any space dimension <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>≥</mo><mn>3</mn></mrow></semantics></math></inline-formula>, the decay and scattering in the energy space for the solution to the damped nonlinear Schrödinger equation posed on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>d</mi></msup><mo>×</mo><mi mathvariant="double-struck">T</mi></mrow></semantics></math></inline-formula> and initial data in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>H</mi><mn>1</mn></msup><mrow><mo>(</mo><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>d</mi></msup><mo>×</mo><mi mathvariant="double-struck">T</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. We will also derive new bilinear Morawetz identities and corresponding localized Morawetz estimates.https://www.mdpi.com/2075-1680/14/6/447nonlinear Schrödinger equationsSchrödinger operatorsscattering theorylocal nonlinearitydamping |
| spellingShingle | Taim Saker Mirko Tarulli George Venkov Scattering in the Energy Space for Solutions of the Damped Nonlinear Schrödinger Equation on <inline-formula><math display="inline"><semantics><mrow><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>d</mi></msup><mo>×</mo><mi mathvariant="double-struck">T</mi></mrow></semantics></math></inline-formula> Axioms nonlinear Schrödinger equations Schrödinger operators scattering theory local nonlinearity damping |
| title | Scattering in the Energy Space for Solutions of the Damped Nonlinear Schrödinger Equation on <inline-formula><math display="inline"><semantics><mrow><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>d</mi></msup><mo>×</mo><mi mathvariant="double-struck">T</mi></mrow></semantics></math></inline-formula> |
| title_full | Scattering in the Energy Space for Solutions of the Damped Nonlinear Schrödinger Equation on <inline-formula><math display="inline"><semantics><mrow><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>d</mi></msup><mo>×</mo><mi mathvariant="double-struck">T</mi></mrow></semantics></math></inline-formula> |
| title_fullStr | Scattering in the Energy Space for Solutions of the Damped Nonlinear Schrödinger Equation on <inline-formula><math display="inline"><semantics><mrow><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>d</mi></msup><mo>×</mo><mi mathvariant="double-struck">T</mi></mrow></semantics></math></inline-formula> |
| title_full_unstemmed | Scattering in the Energy Space for Solutions of the Damped Nonlinear Schrödinger Equation on <inline-formula><math display="inline"><semantics><mrow><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>d</mi></msup><mo>×</mo><mi mathvariant="double-struck">T</mi></mrow></semantics></math></inline-formula> |
| title_short | Scattering in the Energy Space for Solutions of the Damped Nonlinear Schrödinger Equation on <inline-formula><math display="inline"><semantics><mrow><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>d</mi></msup><mo>×</mo><mi mathvariant="double-struck">T</mi></mrow></semantics></math></inline-formula> |
| title_sort | scattering in the energy space for solutions of the damped nonlinear schrodinger equation on inline formula math display inline semantics mrow msup mrow mi mathvariant double struck r mi mrow mi d mi msup mo mo mi mathvariant double struck t mi mrow semantics math inline formula |
| topic | nonlinear Schrödinger equations Schrödinger operators scattering theory local nonlinearity damping |
| url | https://www.mdpi.com/2075-1680/14/6/447 |
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