{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:44:28Z","timestamp":1777448668216,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"3-4","license":[{"start":{"date-parts":[[2008,4,1]],"date-time":"2008-04-01T00:00:00Z","timestamp":1207008000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2008,4]]},"abstract":"<jats:p>This paper is devoted to the rigorous theory of nonlinear geometric optics for multiple shocks to a general N\u00d7N conservation law in one space variable. For the problem of multiple weak shocks perturbed by small amplitude, high-frequency oscillatory waves, we obtain that the leading profiles of oscillatory shocks are solution to an integro-differential system with free boundaries, the leading terms of shock fronts don't oscillate, and oscillations only appear in the leading terms shock speeds.<\/jats:p>","DOI":"10.3233\/asy-2008-0864","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:00:42Z","timestamp":1575054042000},"page":"143-198","source":"Crossref","is-referenced-by-count":0,"title":["Multiple highly oscillatory shock waves"],"prefix":"10.1177","volume":"57","author":[{"given":"Yahong","family":"Peng","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Donghua University, Shanghai 200051, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ya-Guang","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2008,4,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2008-0864","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2008-0864","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:38:34Z","timestamp":1777379914000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2008-0864"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,4]]},"references-count":0,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2008,4]]}},"alternative-id":["10.3233\/ASY-2008-0864"],"URL":"https:\/\/doi.org\/10.3233\/asy-2008-0864","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,4]]}}}