{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:27:11Z","timestamp":1787340431831,"version":"build-2736575974"},"reference-count":26,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Math."],"published-print":{"date-parts":[[1995,4]]},"abstract":"<jats:p>On a semi-infinite domain, an analytical characterization of exponentially slow internal layer motion for the Allen\u2013Cahn equation and for a singularly perturbed viscous shock problem is given. The results extend some previous results that were restricted to a finite geometry. For these slow motion problems, we show that the slow dynamics associated with the semi-infinite domain are not preserved, even qualitatively, by imposing a commonly used form of artificial boundary condition to truncate the semi-infinite domain to a finite domain. This extreme sensitivity to boundary conditions and domain truncation is a direct result of the exponential ill-conditioning of the underlying linearized problem. For Burgers equation, many of the analytical results are verified by calculating certain explicit solutions. Some related ill-conditioned internal layer problems are examined.<\/jats:p>","DOI":"10.1137\/s0036139993269254","type":"journal-article","created":{"date-parts":[[2005,2,24]],"date-time":"2005-02-24T02:55:41Z","timestamp":1109213741000},"page":"425-445","source":"Crossref","is-referenced-by-count":15,"title":["Internal Layers, Small Eigenvalues, and the Sensitivity of Metastable Motion"],"prefix":"10.1137","volume":"55","author":[{"given":"Michael J.","family":"Ward","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luis G.","family":"Reyna","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,5]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1002\/sapm1970493277"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/0521070"},{"key":"R3","volume-title":"Numerical solution of initial value problems in differential-algebraic equations","author":"Brenan K.","year":"1989"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5160-6_11"},{"key":"R5","first-page":"155","volume":"44","author":"Caginalp Gunduz","year":"1986","journal-title":"Quart. Appl. Math."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160420502"},{"key":"R7","volume-title":"Ordinary Differential Equations","author":"Carrier G.","year":"1968"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/0511001"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/0150029"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/BF01048791"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/0132047"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/0723063"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1137\/0907065"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1002\/sapm198777161"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1016\/0168-9274(86)90026-7"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1137\/0141029"},{"key":"R17","unstructured":"J. G. Laforgue, R. E. O'Malley,  The Supersensitivity of the Shock Layer Location for Burgers Equation,  manuscript presented at the First Panamerican Workshop in Applied and Computational Mathematics,  1993, January"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-1810-1_13"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1002\/sapm1983683227"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1137\/1017005"},{"key":"R21","unstructured":"J. Neu,  1984, Unpublished lecture notes"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1017\/S0956792500001583"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160480202"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1080\/01630569508816628"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1002\/sapm199287295"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1137\/0141023"}],"container-title":["SIAM Journal on Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0036139993269254","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:34:55Z","timestamp":1787337295000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0036139993269254"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,4]]},"references-count":26,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1995,4]]}},"alternative-id":["10.1137\/S0036139993269254"],"URL":"https:\/\/doi.org\/10.1137\/s0036139993269254","relation":{},"ISSN":["0036-1399","1095-712X"],"issn-type":[{"value":"0036-1399","type":"print"},{"value":"1095-712X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,4]]}}}