{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,15]],"date-time":"2025-11-15T17:13:12Z","timestamp":1763226792735,"version":"3.40.5"},"reference-count":41,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,1,9]],"date-time":"2020-01-09T00:00:00Z","timestamp":1578528000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,1,9]]},"abstract":"<jats:p>In this paper, we study the nonlinear adaptive boundary control problem of the modified generalized Korteweg\u2013de Vries\u2013Burgers equation (MGKdVB) when the spatial domain is <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mfenced open=\"[\" close=\"]\" separators=\"|\"><mml:mrow><mml:mn>0,1<\/mml:mn><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:math>. Four different nonlinear adaptive control laws are designed for the MGKdVB equation without assuming the nullity of the physical parameters <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi>\u03bd<\/mml:mi><\/mml:math>, <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mi>\u03bc<\/mml:mi><\/mml:math>, <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:msub><mml:mrow><mml:mi>\u03b3<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>, and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:msub><mml:mrow><mml:mi>\u03b3<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math> and depending whether these parameters are known or unknown. Then, using Lyapunov theory, the <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:msup><mml:mrow><mml:mi>L<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>-global exponential stability of the solution is proven in each case. Finally, numerical simulations are presented to illustrate the developed control schemes.<\/jats:p>","DOI":"10.1155\/2020\/4574257","type":"journal-article","created":{"date-parts":[[2020,1,9]],"date-time":"2020-01-09T18:31:08Z","timestamp":1578594668000},"page":"1-18","source":"Crossref","is-referenced-by-count":5,"title":["Nonlinear Adaptive Boundary Control of the Modified Generalized Korteweg\u2013de Vries\u2013Burgers Equation"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9365-449X","authenticated-orcid":true,"given":"B.","family":"Chentouf","sequence":"first","affiliation":[{"name":"Department of Mathematics, Kuwait University, P. O. Box 5969, Safat, Kuwait City 13060, Kuwait"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0655-9908","authenticated-orcid":true,"given":"N.","family":"Smaoui","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kuwait University, P. O. Box 5969, Safat, Kuwait City 13060, Kuwait"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Alalabi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kuwait University, P. O. 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