{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:21:04Z","timestamp":1776784864646,"version":"3.51.2"},"reference-count":30,"publisher":"American Mathematical Society (AMS)","issue":"253","license":[{"start":{"date-parts":[[2006,10,21]],"date-time":"2006-10-21T00:00:00Z","timestamp":1161388800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We prove the convergence of a semi-implicit monotone finite difference scheme approximating an initial-boundary value problem for a spatially one-dimensional quasilinear strongly degenerate parabolic equation, which is supplied with two different inhomogeneous flux-type boundary conditions. This problem arises in the modeling of the sedimentation-consolidation process. We formulate the definition of entropy solution of the model in the sense of Kru\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"ModifyingAbove z With \u02c7\">\n                        <mml:semantics>\n                          <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                            <mml:mover>\n                              <mml:mstyle displaystyle=\"false\" scriptlevel=\"0\">\n                                <mml:mtext>z<\/mml:mtext>\n                              <\/mml:mstyle>\n                              <mml:mo stretchy=\"false\">\n                                \u02c7\n                                \n                              <\/mml:mo>\n                            <\/mml:mover>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\check {\\mbox {z}}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    kov and prove convergence of the scheme to the unique\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper B upper V\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>B<\/mml:mi>\n                            <mml:mi>V<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">BV<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    entropy solution of the problem, up to satisfaction of one of the boundary conditions.\n                  <\/p>","DOI":"10.1090\/s0025-5718-05-01787-4","type":"journal-article","created":{"date-parts":[[2005,11,16]],"date-time":"2005-11-16T10:22:35Z","timestamp":1132136555000},"page":"91-112","source":"Crossref","is-referenced-by-count":18,"title":["A semi-implicit monotone difference scheme for an initial-boundary value problem of a strongly degenerate parabolic equation modeling sedimentation-consolidation processes"],"prefix":"10.1090","volume":"75","author":[{"given":"Raimund","family":"B\u00fcrger","sequence":"first","affiliation":[]},{"given":"An\u00edbal","family":"Coronel","sequence":"additional","affiliation":[]},{"given":"Mauricio","family":"Sep\u00falveda","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2005,10,21]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1137\/S0036139902408163","article-title":"Strongly degenerate parabolic-hyperbolic systems modeling polydisperse sedimentation with compression","volume":"64","author":"Berres, Stefan","year":"2003","journal-title":"SIAM J. 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