{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T02:28:00Z","timestamp":1649039280794},"reference-count":23,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2015]]},"abstract":"<jats:p>This paper deals essentially with a nonlinear degenerate evolution equation of the form<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>K<\/mml:mi><mml:msup><mml:mrow><mml:mi>u<\/mml:mi><\/mml:mrow><mml:mrow><mml:mo>\u2033<\/mml:mo><\/mml:mrow><\/mml:msup><mml:mo>-<\/mml:mo><mml:mi mathvariant=\"normal\">\u0394<\/mml:mi><mml:mi>u<\/mml:mi><mml:mo>+<\/mml:mo><mml:mrow><mml:msubsup><mml:mo stretchy=\"false\">\u2211<\/mml:mo><mml:mrow><mml:mi>j<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:msubsup><mml:mrow><mml:msub><mml:mrow><mml:mi>b<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>j<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:mrow><mml:mfenced separators=\"|\"><mml:mrow><mml:mo>\u2202<\/mml:mo><mml:msup><mml:mrow><mml:mi>u<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>\u2032<\/mml:mi><\/mml:mrow><\/mml:msup><mml:mo>\/<\/mml:mo><mml:mo>\u2202<\/mml:mo><mml:msub><mml:mrow><mml:mi>x<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>j<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:mfenced><mml:mo>+<\/mml:mo><mml:msup><mml:mrow><mml:mfenced open=\"|\" close=\"|\" separators=\"|\"><mml:mrow><mml:mi>u<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:mrow><mml:mrow><mml:mi>\u03c3<\/mml:mi><\/mml:mrow><\/mml:msup><mml:mi>u<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:math>supplemented with nonlinear boundary conditions of Neumann type given by<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi>\u2202<\/mml:mi><mml:mi>u<\/mml:mi><mml:mo>\/<\/mml:mo><mml:mi>\u2202<\/mml:mi><mml:mi>\u03bd<\/mml:mi><mml:mo>+<\/mml:mo><mml:mi>h<\/mml:mi><mml:mfenced separators=\"|\"><mml:mrow><mml:mo>\u00b7<\/mml:mo><mml:mo>,<\/mml:mo><mml:mi>\u00a0<\/mml:mi><mml:msup><mml:mrow><mml:mi>u<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>\u2032<\/mml:mi><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:mfenced><mml:mo>=<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:math>. Under suitable conditions the existence and uniqueness of solutions are shown and that the boundary damping produces a uniform global stability of the corresponding solutions.<\/jats:p>","DOI":"10.1155\/2015\/281032","type":"journal-article","created":{"date-parts":[[2015,3,3]],"date-time":"2015-03-03T16:01:18Z","timestamp":1425398478000},"page":"1-13","source":"Crossref","is-referenced-by-count":1,"title":["On a Nonlinear Degenerate Evolution Equation with Nonlinear Boundary Damping"],"prefix":"10.1155","volume":"2015","author":[{"given":"A. T.","family":"Lour\u00eado","sequence":"first","affiliation":[{"name":"DM-UEPB, Campina Grande, PB, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G.","family":"Siracusa","sequence":"additional","affiliation":[{"name":"DMA-S\u00e3o Crist\u00f3v\u00e3o, SE, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C. 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