{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T06:40:27Z","timestamp":1776753627770,"version":"3.51.2"},"reference-count":13,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2016,6,1]],"date-time":"2016-06-01T00:00:00Z","timestamp":1464739200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Bull Braz Math Soc, New Series"],"published-print":{"date-parts":[[2016,6]]},"DOI":"10.1007\/s00574-016-0168-4","type":"journal-article","created":{"date-parts":[[2016,6,22]],"date-time":"2016-06-22T14:11:02Z","timestamp":1466604662000},"page":"545-559","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Loss of hyperbolicity changes the number of wave groups in Riemann problems"],"prefix":"10.1007","volume":"47","author":[{"given":"Vitor","family":"Matos","sequence":"first","affiliation":[]},{"given":"Julio D.","family":"Silva","sequence":"additional","affiliation":[]},{"given":"Dan","family":"Marchesin","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,6,22]]},"reference":[{"key":"168_CR1","volume-title":"Structural stability of nonlinear waves for conservation laws","author":"F. Furtado","year":"1989","unstructured":"F. Furtado. Structural stability of nonlinear waves for conservation laws. Ph. D. thesis, NYU (1989)."},{"issue":"4","key":"168_CR2","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1137\/0521047","volume":"21","author":"E. Isaacson","year":"1990","unstructured":"E. Isaacson, D. Marchesin and B. Plohr. Transitional waves for conservation laws. SIAM J. Math. Anal., 21(4) (1990), 837\u2013866.","journal-title":"SIAM J. Math. Anal."},{"issue":"2","key":"168_CR3","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1016\/0022-0396(86)90037-9","volume":"65","author":"E. L. Isaacson","year":"1986","unstructured":"E. L. Isaacson and J. B. Temple. Analysis of a singular hyperbolic system of conservation laws. Journal of Differential Equations, 65(2) (1986), 250\u2013268.","journal-title":"Journal of Differential Equations"},{"issue":"3","key":"168_CR4","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1137\/0519039","volume":"19","author":"T. Johansen","year":"1988","unstructured":"T. Johansen and R. Winther. The solution of the Riemann problem for a hyperbolic system of conservation laws modeling polymer flooding. SIAM J. Math. Anal., 19(3) (1988), 541\u2013566.","journal-title":"SIAM J. Math. Anal."},{"key":"168_CR5","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/BF00281590","volume":"72","author":"B. Keyfitz","year":"1980","unstructured":"B. Keyfitz and H. Kranzer. A system of non-strictly hyperbolic conservation laws arising in elasticity theory. Arch. Rational Mech. Anal., 72 (1980), 219\u2013241.","journal-title":"Arch. Rational Mech. Anal."},{"key":"168_CR6","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1002\/cpa.3160100406","volume":"10","author":"P. Lax","year":"1957","unstructured":"P. Lax. Hyperbolic systems of conservation laws II. Comm. Pure Appl. Math., 10 (1957), 537\u2013566.","journal-title":"Pure Appl. Math."},{"key":"168_CR7","first-page":"89","volume":"199","author":"T.-P. Liu","year":"1974","unstructured":"T.-P. Liu. The Riemann problem for general 2\u00d72 conservation laws. Trans. AMS, 199 (1974), 89\u2013112.","journal-title":"Trans. AMS"},{"issue":"1","key":"168_CR8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0022-0396(85)90068-3","volume":"57","author":"T. P. Liu","year":"1985","unstructured":"T. P. Liu and C. H. Wang. On a nonstrictly hyperbolic system of conservation laws. J. Differential Equations, 57(1) (1985), 1\u201314.","journal-title":"J. Differential Equations"},{"key":"168_CR9","unstructured":"Maplesoft. Maple 13, 2009,Maplesoft, a division ofWaterlooMaple Inc,Waterloo, Ontario, Canada."},{"key":"168_CR10","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1142\/S0219891608001477","volume":"2","author":"V. Matos","year":"2008","unstructured":"V. Matos and D. Marchesin. Large viscous solutions for small data in systems of conservation laws that change type. J. Hyperb. Diff. Eq., 2 (2008), 257\u2013278.","journal-title":"J. Hyperb. Diff. Eq."},{"key":"168_CR11","volume-title":"Organizing structures in the Riemann solution for thermal multiphase flow in porous media","author":"J. D. Silva","year":"2011","unstructured":"J. D. Silva. Organizing structures in the Riemann solution for thermal multiphase flow in porous media. Ph. D. thesis, IMPA, Brazil (2011)."},{"issue":"4","key":"168_CR12","doi-asserted-by":"crossref","first-page":"1295","DOI":"10.1016\/j.jde.2013.10.005","volume":"256","author":"J. D. Silva","year":"2014","unstructured":"J. D. Silva and D. Marchesin. Riemann solutions without an intermediate constant state for a system of two conservation laws. Journal of Differential Equations, 256(4) (2014), 1295\u20131316.","journal-title":"Journal of Differential Equations"},{"issue":"2","key":"168_CR13","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1006\/jdeq.1996.0053","volume":"126","author":"S. Schecter","year":"1996","unstructured":"S. Schecter, D. Marchesin and B. J. Plohr. Structurally stable Riemann solutions. Journal of Differential Equations, 126(2) (1996), 303\u2013354.","journal-title":"Journal of Differential Equations"}],"container-title":["Bulletin of the Brazilian Mathematical Society, New Series"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00574-016-0168-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00574-016-0168-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00574-016-0168-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,24]],"date-time":"2017-06-24T12:49:56Z","timestamp":1498308596000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00574-016-0168-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6]]},"references-count":13,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,6]]}},"alternative-id":["168"],"URL":"https:\/\/doi.org\/10.1007\/s00574-016-0168-4","relation":{},"ISSN":["1678-7544","1678-7714"],"issn-type":[{"value":"1678-7544","type":"print"},{"value":"1678-7714","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,6]]}}}