{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T23:42:53Z","timestamp":1778283773518,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2015,2,1]],"date-time":"2015-02-01T00:00:00Z","timestamp":1422748800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2015,2]]},"abstract":"<jats:p>\n                    We study the existence, uniqueness and asymptotic expansions to perturbed Poisson\u2013Boltzmann equations on an unbounded domain in R\n                    <jats:sup>2<\/jats:sup>\n                    or R\n                    <jats:sup>3<\/jats:sup>\n                    . First, a shooting method is applied to prove the existence and uniqueness of the exact solution. For the approximation to the regularly perturbed Poisson\u2013Boltzmann equation, the solution via the classical method fails. We develop a novel approximate solution in terms of generalized asymptotic expansions. For the singularly perturbed problem, we show that a formula of asymptotic expansions with a boundary layer near the left end point provides a valid approximation. All our results are proved rigorously.\n                  <\/jats:p>","DOI":"10.3233\/asy-141262","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:38:03Z","timestamp":1575056283000},"page":"125-146","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":5,"title":["Asymptotic analysis of the perturbed Poisson\u2013Boltzmann equation on unbounded domains"],"prefix":"10.1177","volume":"91","author":[{"given":"Manjun","family":"Ma","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Sciences, China Jiliang University, Hangzhou, Zhejiang, China. E-mail: mmj@cjlu.edu.cn"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunhua","family":"Ou","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Memorial University, St. John's, NL, Canada. E-mail: ou@mun.ca"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2015,2,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-141262","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-141262","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:40:21Z","timestamp":1777380021000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-141262"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,2]]}},"alternative-id":["10.3233\/ASY-141262"],"URL":"https:\/\/doi.org\/10.3233\/asy-141262","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2]]}}}