Exponential decay estimates for the damped defocusing Schrödinger equation in exterior domains
We are concerned with the existence as well as the exponential stability in H1-level for the damped defocusing Schrödinger equation posed in a two-dimensional exterior domain Ω with smooth boundary ∂Ω. The proofs of the existence are based on the properties of pseudo-differential operators introduce...
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| Veröffentlicht in: | Journal of mathematical physics 2023-10, Vol.64 (10) |
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| creator | Cavalcanti, Marcelo M. Corrêa, Wellington J. Domingos Cavalcanti, Valéria Neves |
| description | We are concerned with the existence as well as the exponential stability in H1-level for the damped defocusing Schrödinger equation posed in a two-dimensional exterior domain Ω with smooth boundary ∂Ω. The proofs of the existence are based on the properties of pseudo-differential operators introduced in Dehman et al. [Math. Z. 254, 729–749 (2006)] and a Strichartz estimate proved by Anton [Bull. Soc. Math. Fr. 136, 27–65 (2008)], while the exponential stability is achieved by combining arguments firstly considered by Zuazua [J. Math. Pures Appl. 9, 513–529 (1991)] for the wave equation adapted to the present context and a global uniqueness theorem. In addition, we proved propagation results for the linear Schrödinger equation for any dimensional and for any (reasonable) boundary conditions employing microlocal analysis. |
| doi_str_mv | 10.1063/5.0101506 |
| format | Article |
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The proofs of the existence are based on the properties of pseudo-differential operators introduced in Dehman et al. [Math. Z. 254, 729–749 (2006)] and a Strichartz estimate proved by Anton [Bull. Soc. Math. Fr. 136, 27–65 (2008)], while the exponential stability is achieved by combining arguments firstly considered by Zuazua [J. Math. Pures Appl. 9, 513–529 (1991)] for the wave equation adapted to the present context and a global uniqueness theorem. 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In addition, we proved propagation results for the linear Schrödinger equation for any dimensional and for any (reasonable) boundary conditions employing microlocal analysis.</description><subject>Boundary conditions</subject><subject>Defocusing</subject><subject>Differential equations</subject><subject>Operators (mathematics)</subject><subject>Physics</subject><subject>Schrodinger equation</subject><subject>Smooth boundaries</subject><subject>Stability</subject><subject>Uniqueness theorems</subject><subject>Wave equations</subject><issn>0022-2488</issn><issn>1089-7658</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kMtKAzEUhoMoWKsL3yDgSmFq7pNZSqkXKLhQ1yHNxaa0M9MkA-2L-QK-mNF27eocON85h-8H4BqjCUaC3vMJwghzJE7ACCPZVLXg8hSMECKkIkzKc3CR0gohjCVjI6Bmu75rXZuDXkPrjN5Dl3LY6OwS9F2Eeemg1Zve2TL2nRlSaD_hm1nG7y9bWheh2w46h66FoYVul10MZc92Gx3adAnOvF4nd3WsY_DxOHufPlfz16eX6cO8MoSTXFlZS-T1gmJqiCAUEccJZr4xxmunqRfeGCOoaAwX1mG0YIyK2jSW0AWWko7BzeFuH7vtUBTUqhtiW14qImvMCKt5U6jbA2Vil1J0XvWxuMa9wkj95qe4OuZX2LsDm0zIf37_wD-GiHEq</recordid><startdate>20231001</startdate><enddate>20231001</enddate><creator>Cavalcanti, Marcelo M.</creator><creator>Corrêa, Wellington J.</creator><creator>Domingos Cavalcanti, Valéria Neves</creator><general>American Institute of Physics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><orcidid>https://orcid.org/0000-0001-5493-5918</orcidid><orcidid>https://orcid.org/0000-0001-5638-3272</orcidid><orcidid>https://orcid.org/0000-0002-1047-3763</orcidid></search><sort><creationdate>20231001</creationdate><title>Exponential decay estimates for the damped defocusing Schrödinger equation in exterior domains</title><author>Cavalcanti, Marcelo M. ; Corrêa, Wellington J. ; Domingos Cavalcanti, Valéria Neves</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c252t-d8780fab313c262302e5214f9ccfaea3f6fccc6369c56de10b44367c9d23b1883</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Boundary conditions</topic><topic>Defocusing</topic><topic>Differential equations</topic><topic>Operators (mathematics)</topic><topic>Physics</topic><topic>Schrodinger equation</topic><topic>Smooth boundaries</topic><topic>Stability</topic><topic>Uniqueness theorems</topic><topic>Wave equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cavalcanti, Marcelo M.</creatorcontrib><creatorcontrib>Corrêa, Wellington J.</creatorcontrib><creatorcontrib>Domingos Cavalcanti, Valéria Neves</creatorcontrib><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Journal of mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Cavalcanti, Marcelo M.</au><au>Corrêa, Wellington J.</au><au>Domingos Cavalcanti, Valéria Neves</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Exponential decay estimates for the damped defocusing Schrödinger equation in exterior domains</atitle><jtitle>Journal of mathematical physics</jtitle><date>2023-10-01</date><risdate>2023</risdate><volume>64</volume><issue>10</issue><issn>0022-2488</issn><eissn>1089-7658</eissn><coden>JMAPAQ</coden><abstract>We are concerned with the existence as well as the exponential stability in H1-level for the damped defocusing Schrödinger equation posed in a two-dimensional exterior domain Ω with smooth boundary ∂Ω. 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| source | AIP Journals Complete; Alma/SFX Local Collection |
| subjects | Boundary conditions Defocusing Differential equations Operators (mathematics) Physics Schrodinger equation Smooth boundaries Stability Uniqueness theorems Wave equations |
| title | Exponential decay estimates for the damped defocusing Schrödinger equation in exterior domains |
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