Pub Date : 2023-02-14DOI: 10.1007/s42985-022-00222-y
C. O. Alves, Tahir Boudjeriou
{"title":"Existence and uniqueness of solution for some time fractional parabolic equations involving the 1-Laplace operator","authors":"C. O. Alves, Tahir Boudjeriou","doi":"10.1007/s42985-022-00222-y","DOIUrl":"https://doi.org/10.1007/s42985-022-00222-y","url":null,"abstract":"","PeriodicalId":74818,"journal":{"name":"SN partial differential equations and applications","volume":"1 1","pages":"1-35"},"PeriodicalIF":0.0,"publicationDate":"2023-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90821736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-13DOI: 10.1007/s42985-022-00221-z
Danilo F. da Silva, E. Lima, H. D. de Lima
{"title":"Some maximum principles for the drift Laplacian applied to complete spacelike hypersurfaces","authors":"Danilo F. da Silva, E. Lima, H. D. de Lima","doi":"10.1007/s42985-022-00221-z","DOIUrl":"https://doi.org/10.1007/s42985-022-00221-z","url":null,"abstract":"","PeriodicalId":74818,"journal":{"name":"SN partial differential equations and applications","volume":"81 1","pages":"1-16"},"PeriodicalIF":0.0,"publicationDate":"2023-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83428311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01Epub Date: 2023-06-29DOI: 10.1007/s42985-023-00241-3
Raphael Winter
We prove the existence of stationary solutions for the density of an infinitely extended plasma interacting with an arbitrary configuration of background charges. Furthermore, we show that the solution cannot be unique if the total charge of the background is attractive. In this case, infinitely many different stationary solutions exist. The non-uniqueness can be explained by the presence of trapped particles orbiting the attractive background charge.
{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\">Existence and non-uniqueness of stationary states for the Vlasov-Poisson equation on <ns0:math><ns0:msup><ns0:mrow><ns0:mi>R</ns0:mi></ns0:mrow><ns0:mn>3</ns0:mn></ns0:msup></ns0:math> subject to attractive background charges.","authors":"Raphael Winter","doi":"10.1007/s42985-023-00241-3","DOIUrl":"10.1007/s42985-023-00241-3","url":null,"abstract":"<p><p>We prove the existence of stationary solutions for the density of an infinitely extended plasma interacting with an arbitrary configuration of background charges. Furthermore, we show that the solution cannot be unique if the total charge of the background is attractive. In this case, infinitely many different stationary solutions exist. The non-uniqueness can be explained by the presence of trapped particles orbiting the attractive background charge.</p>","PeriodicalId":74818,"journal":{"name":"SN partial differential equations and applications","volume":"4 4","pages":"30"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10310580/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10123698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-16DOI: 10.1007/s42985-022-00220-0
L. Setayeshgar
{"title":"Uniform large deviations for a class of semilinear stochastic partial differential equations driven by a Brownian sheet","authors":"L. Setayeshgar","doi":"10.1007/s42985-022-00220-0","DOIUrl":"https://doi.org/10.1007/s42985-022-00220-0","url":null,"abstract":"","PeriodicalId":74818,"journal":{"name":"SN partial differential equations and applications","volume":"1 1","pages":"1-12"},"PeriodicalIF":0.0,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83111588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-13DOI: 10.1007/s42985-022-00219-7
Young-Pil Choi
{"title":"On the rigorous derivation of hydrodynamics of the Kuramoto model for synchronization phenomena","authors":"Young-Pil Choi","doi":"10.1007/s42985-022-00219-7","DOIUrl":"https://doi.org/10.1007/s42985-022-00219-7","url":null,"abstract":"","PeriodicalId":74818,"journal":{"name":"SN partial differential equations and applications","volume":"21 1","pages":"1-20"},"PeriodicalIF":0.0,"publicationDate":"2022-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91179605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-23DOI: 10.1007/s42985-022-00216-w
K. D. Searle, J. V. van Vuuren
{"title":"A time-periodic reaction-diffusion population model of a species subjected to harvesting on the boundary of a protected habitat","authors":"K. D. Searle, J. V. van Vuuren","doi":"10.1007/s42985-022-00216-w","DOIUrl":"https://doi.org/10.1007/s42985-022-00216-w","url":null,"abstract":"","PeriodicalId":74818,"journal":{"name":"SN partial differential equations and applications","volume":"18 1","pages":"1-19"},"PeriodicalIF":0.0,"publicationDate":"2022-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82506577","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}