{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T00:48:40Z","timestamp":1773794920371,"version":"3.50.1"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"4","license":[{"start":{"date-parts":[[2010,1,1]],"date-time":"2010-01-01T00:00:00Z","timestamp":1262304000000},"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":[[2010]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>\n        We have studied the stability of finite-difference schemes approximating\n        boundary value problems for parabolic equations with a nonlinear and nonmonotonic\n        source of the power type. We have obtained simple sufficient input data conditions, in\n        which the solution of the differential problem is globally stable for all 0 \u2264 t \u2264 +\u221e. It is\n        shown that if these conditions fail, then the solution can blow up (go to infinity) in finite\n        time. The lower bound of the blow up time has been determined. The stability of the\n        solution of BVP for the nonlinear convection-diffusion equation has been investigated.\n        In all cases, we used the method of energy inequalities based on the application of\n        the Chaplygin comparison theorem for nonlinear differential equations, Bihari-type\n        inequalities and their discrete analogs.<\/jats:p>","DOI":"10.2478\/cmam-2010-0024","type":"journal-article","created":{"date-parts":[[2013,4,15]],"date-time":"2013-04-15T16:18:58Z","timestamp":1366042738000},"page":"395-421","source":"Crossref","is-referenced-by-count":7,"title":["Well-Posedness and Blow Up for IBVP for Semilinear Parabolic Equations and Numerical Methods"],"prefix":"10.2478","volume":"10","author":[{"given":"P.","family":"Matus","sequence":"first","affiliation":[{"name":"1Institute of Mathematics, National Academy of Sciences 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, National Academy of Sciences of Belarus, 11 Surganov Str., 220072 Minsk, Belarus."}]},{"given":"A.","family":"Kandratsiuk","sequence":"additional","affiliation":[{"name":"3Belarusian State University, 4, Nezavisimosti Ave., 220030, Minsk, Belarus."}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/10\/4\/article-p395.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/cmam-2010-0024\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T14:21:45Z","timestamp":1619101305000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/10\/4\/article-p395.xml"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010]]},"references-count":0,"journal-issue":{"issue":"4"},"URL":"https:\/\/doi.org\/10.2478\/cmam-2010-0024","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2010]]}}}