{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T10:42:56Z","timestamp":1776768176362,"version":"3.51.2"},"reference-count":29,"publisher":"American Mathematical Society (AMS)","issue":"215","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    This paper is to study the asymptotic stability of stationary discrete shocks for the Lax-Friedrichs scheme approximating nonconvex scalar conservation laws, provided that the summations of the initial perturbations equal to zero. The result is proved by using a weighted energy method based on the nonconvexity. Moreover, the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"l Superscript 1\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>l<\/mml:mi>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">l^1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    stability is also obtained. The key points of our proofs are to choose a suitable weight function.\n                  <\/p>","DOI":"10.1090\/s0025-5718-96-00733-8","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"1137-1153","source":"Crossref","is-referenced-by-count":3,"title":["Nonlinear stability of stationary discrete shocks for nonconvex scalar conservation laws"],"prefix":"10.1090","volume":"65","author":[{"given":"Hailiang","family":"Liu","sequence":"first","affiliation":[]},{"given":"Jinghua","family":"Wang","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1996]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1016\/S0252-9602(18)30535-6","article-title":"Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics. III","volume":"6","author":"Chen, Gui Qiang","year":"1986","journal-title":"Acta Math. Sci. 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