{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T12:43:24Z","timestamp":1768740204120,"version":"3.49.0"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Math."],"published-print":{"date-parts":[[2014,1]]},"abstract":"<jats:p>In the setting of a product of distributions which is not defined by approximation processes, we are able to consider a Riemann problem for the system u<jats:sub>t<\/jats:sub>+ [\u03d5(u)]<jats:sub>x<\/jats:sub>= 0, v<jats:sub>t<\/jats:sub>+ [\u03c8(u)v]<jats:sub>x<\/jats:sub>= 0, with the unknown states u, v in convenient spaces of distributions and \u03d5, \u03c8 : \u211d \u2192 \u211d continuous. A consistent extension of the classical solution concept will show the possible arising of a \u03b4-shock wave solution. This procedure affords a simpler and more general framework to construct singular solutions and can surely be applied to other equations or systems.<\/jats:p>","DOI":"10.1142\/s0129167x14500074","type":"journal-article","created":{"date-parts":[[2014,1,6]],"date-time":"2014-01-06T04:06:13Z","timestamp":1388981173000},"page":"1450007","source":"Crossref","is-referenced-by-count":33,"title":["A DISTRIBUTIONAL PRODUCT APPROACH TO \u03b4-SHOCK WAVE SOLUTIONS FOR A GENERALIZED PRESSURELESS GAS DYNAMICS SYSTEM"],"prefix":"10.1142","volume":"25","author":[{"given":"C. O. R.","family":"SARRICO","sequence":"first","affiliation":[{"name":"CMAF, University of Lisbon, Av. Prof. Gama Pinto 2, 1649-003, Lisboa-, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2014,2,9]]},"reference":[{"key":"rf1","first-page":"2173","volume":"24","author":"Bouchut F.","journal-title":"Comm. Partial Differential Equations"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142997317353"},{"key":"rf3","first-page":"641","volume":"2","author":"Bressan A.","journal-title":"Boll. Unione Mat. Ital. B (7)"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141001399350"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1063\/1.528069"},{"key":"rf6","first-page":"483","volume":"74","author":"Dal Maso G.","journal-title":"J. Math. Pures Appl."},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2008.03.006"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2004.12.011"},{"key":"rf10","first-page":"401","volume":"29","author":"Danilov V. G.","journal-title":"Quart. Appl. Math."},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1081\/PDE-200050026"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1995.1080"},{"key":"rf16","doi-asserted-by":"crossref","first-page":"904","DOI":"10.1002\/mma.1226","volume":"33","author":"Mitrovic D.","journal-title":"Math. Methods Appl. Sci."},{"key":"rf17","first-page":"145","volume":"54","author":"Nedeljkov M.","journal-title":"Mat. Vesnik"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1002\/mma.480"},{"key":"rf19","first-page":"1143","volume":"334","author":"Nedeljkov M.","journal-title":"J. Math. Anal. Appl."},{"key":"rf20","first-page":"295","volume":"45","author":"Sarrico C. O. R.","journal-title":"Port. Math."},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-247X(03)00187-2"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2005.06.037"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2010.06.036"},{"key":"rf24","first-page":"999","volume":"6","author":"Sarrico C. O. R.","journal-title":"Int. J. Math. Anal."},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1134\/S1061920812020100"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1007\/s11401-012-0713-4"}],"container-title":["International Journal of Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129167X14500074","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,22]],"date-time":"2024-05-22T15:28:52Z","timestamp":1716391732000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129167X14500074"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1]]},"references-count":22,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2014,2,9]]},"published-print":{"date-parts":[[2014,1]]}},"alternative-id":["10.1142\/S0129167X14500074"],"URL":"https:\/\/doi.org\/10.1142\/s0129167x14500074","relation":{},"ISSN":["0129-167X","1793-6519"],"issn-type":[{"value":"0129-167X","type":"print"},{"value":"1793-6519","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1]]}}}