@Article{ChertovskihChiPodRemZhe:2014:ExUnAn,
               author = "Chertovskih, R. and Chian, Abraham Chian-Long and Podvigina, O. 
                         and Rempel, E. L. and Zheligovsky, V.",
          affiliation = "Institute of Earthquake Prediction Theory and Mathematical 
                         Geophysics, Russian Academy of Sciences, 84/32 Profsoyuznaya St., 
                         117997 Moscow, Russian Federation; Centre for Wind Energy and 
                         Atmospheric Flows, Faculdade de Engenharia da Universidade do 
                         Porto, Rua Dr. Roberto Frias s/n, 4200-465 Porto, Portugal and 
                         {Instituto Nacional de Pesquisas Espaciais (INPE)} and Institute 
                         of Earthquake Prediction Theory and Mathematical Geophysics, 
                         Russian Academy of Sciences, 84/32 Profsoyuznaya St., 117997 
                         Moscow, Russian Federation and Institute of Aeronautical 
                         Technology (IEFM/ITA), World Institute for Space Environment 
                         Research (WISER), S{\~a}o Jos{\'e} dos Campos, S{\~a}o Paulo 
                         12228-900, Brazil; National Institute for Space Research (INPE), 
                         P.O. Box 515, S{\~a}o Jos{\'e} dos Campos, S{\~a}o Paulo 
                         12227-010, Brazil and Institute of Earthquake Prediction Theory 
                         and Mathematical Geophysics, Russian Academy of Sciences, 84/32 
                         Profsoyuznaya St., 117997 Moscow, Russian Federation",
                title = "Existence, uniqueness, and analyticity of space-periodic solutions 
                         to the regularized long-wave equation",
              journal = "Advances in Differential Equations",
                 year = "2014",
               volume = "19",
               number = "7-8",
                pages = "725--754",
             keywords = "space-periodic evolutionary, travelling-wave solutions, 
                         regularized long-wave equation.",
             abstract = "We consider space-periodic evolutionary and travelling-wave 
                         solutions to the regularized long-wave equation (RLWE) with 
                         damping and forcing. We establish existence, uniqueness and 
                         smoothness of the evolutionary solutions for smooth initial 
                         conditions, and global in time spatial analyticity of such 
                         solutions for analytical initial conditions. The width of the 
                         analyticity strip decays at most polynomially. We prove existence 
                         of travelling-wave solutions and uniqueness of travelling waves of 
                         a sufficiently small norm. The importance of damping is 
                         demonstrated by showing that the problem of finding 
                         travelling-wave solutions to the undamped RLWE is not well-posed. 
                         Finally, we demonstrate the asymptotic convergence of the power 
                         series expansion of travelling waves for a weak forcing.",
                 issn = "1079-9389",
                label = "scopus 2014-05 ChertovskihChiPodRemZhe:2014:ExUnAn",
             language = "en",
           targetfile = "Chertovskih+_ADE 2014.pdf",
        urlaccessdate = "27 abr. 2024"
}