Geodesic
Asymptotic Behaviour of Solutions to a Nonlinear Third Order P.D.E. Modeling Physical Phenomena
Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 3, pp. 451-468

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The longtime behaviour of the solutions to the initial boundary value problem (1.1)-(1.3) modeling various physical phenomena, either in the autonomous case or in the nonautonomous case, is studied. Conditions guaranteeing ultimately boundedness and conditions guaranteeing nonlinear asymptotic global stability of the null solution are obtained. Boundary conditions, different from (1.2)1-(1.2)2, are also considered (Section 9). 
@article{BUMI_2012_9_5_3_a0,
     author = {Rionero, Salvatore},
     title = {Asymptotic {Behaviour} of {Solutions} to a {Nonlinear} {Third} {Order} {P.D.E.} {Modeling} {Physical} {Phenomena}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {451--468},
     publisher = {mathdoc},
     volume = {Ser. 9, 5},
     number = {3},
     year = {2012},
     zbl = {1282.35073},
     mrnumber = {3051732},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2012_9_5_3_a0/}
}
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Rionero, Salvatore. Asymptotic Behaviour of Solutions to a Nonlinear Third Order P.D.E. Modeling Physical Phenomena. Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 3, pp. 451-468. http://geodesic.mathdoc.fr/item/BUMI_2012_9_5_3_a0/