{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T19:34:09Z","timestamp":1773776049335,"version":"3.50.1"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"3","license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput. Methods Appl. Math."],"published-print":{"date-parts":[[2009]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p> We have proved the difference analogue of a Bihari-type inequality.\nUsing this inequality, we study the stability in C and monotonicity of the difference\nschemes approximating initial-boundary value problems for nonlinear conservation laws\nand multi-dimensional parabolic equations. It has been shown that in the nonlinear\ncase the stability and monotonicity are determined not only by the behavior of the\napproximate solution but also by its difference derivatives appearing in the nonlinear\nterms of the equation. The stability estimates are obtained without any assumptions\nabout the properties of the solution and nonlinear coefficients of the differential problem.\nHere we use restrictions only on input data (initial and boundary conditions and\nthe right-hand side).\nThe sufficient conditions of the shock wave generation is formulated for input data.\nFor the Riemann problem two exact and stable difference schemes are analyzed.<\/jats:p>","DOI":"10.2478\/cmam-2009-0016","type":"journal-article","created":{"date-parts":[[2013,4,15]],"date-time":"2013-04-15T15:51:14Z","timestamp":1366041074000},"page":"253-280","source":"Crossref","is-referenced-by-count":18,"title":["Stability and Monotonicity of Difference Schemes for Nonlinear Scalar Conservation Laws and Multidimensional Quasi-linear Parabolic Equations"],"prefix":"10.2478","volume":"9","author":[{"given":"P.","family":"Matus","sequence":"first","affiliation":[{"name":"1Institute of Mathematics, NAS of Belarus, 11 Surganov Str., 220072 Minsk, Belarus"},{"name":"2Department of Mathematics, the John Paul II Catholic University of Lublin, Al. Raclawickie 14, 20-950 Lublin, Poland."}]},{"given":"S.","family":"Lemeshevsky","sequence":"additional","affiliation":[{"name":"1Institute of Mathematics, NAS of Belarus, 11 Surganov Str., 220072 Minsk, Belarus"}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/9\/3\/article-p253.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/cmam-2009-0016\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T14:21:28Z","timestamp":1619101288000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/9\/3\/article-p253.xml"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"references-count":0,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.2478\/cmam-2009-0016","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2009]]}}}