Unique continuation property for the Rosenau equation
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Abstract
In this work, using an appropriate Carleman-type estimate, we establish a unique continuation result for the Rosenau equation that models the dynamics of dense discrete systems with high order effects.
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References
bibitem{BourgainC}
newblock J. Bourgain,
newblock On the compactness of the support of solutions of dispersive equations,
newblock Internat. Math. Res. Notices, textbf{5(9)} (1997), 437–447.
bibitem{BIM}
newblock E. Bustamante and P. Isaza and J. Mej'ia,
newblock On the support of solutions to the Zakharov-Kuznetsov,
newblock J. Diff. Eq., textbf{251} (2011), 2728–2736.
bibitem{BIM2}
newblock E. Bustamante and P. Isaza and J. Mej'ia,
newblock On uniqueness properties of solutions of the Zakharov-Kuznetsov,
newblock J. Funct. Anal., textbf{264} (2013), 2529–2549.
bibitem{Mah1}
newblock X. Carvajal and M. Panthee,
newblock Unique continuation property for a higher order nonlinear
Schr"odinger equation,
newblock J. Math. Anal. Appl., textbf{303} (2005), 188–207.
bibitem{Mah2}
newblock X. Carvajal and M. Panthee,
newblock On uniqueness of solution for a nonlinear Schr"odinger-Airy equation,
newblock Nonlinear Analysis: Theory, Methods and Applications, textbf{64(1)} (2006), 146–158.
bibitem{Escauriaza}
newblock L. Escauriaza and C. Kenig and G. Ponce and L. Vega,
newblock On uniqueness properties of solutions of the $k$-generalized KdV equations,
newblock J. Funct. Anal., textbf{244(2)} (2007), 504–535.
bibitem{Iorio1}
newblock R. J. I'orio Jr.,
newblock Unique continuation principles for the Benjamin-Ono equation,
newblock Differential Integral Equations, textbf{16(11)} (2003), 1281–1291.
bibitem{Iorio2}
newblock R. J. I'orio Jr.,
newblock Unique Continuation Principles for Some Equations of Benjamin-Ono Type,
newblock Nonlinear Equations: Methods, Models and Applications, textbf{54} (2003), 163–179.
bibitem{Isa}
newblock V. Isakov,
newblock Inverse problems for partial differential equations,
newblock Appal. Math. Sci., 1997.
bibitem{KPV1}
newblock C. Kenig and G. Ponce and L. Vega,
newblock On unique continuation for nonlinear Schr"odinger equation,
newblock Comm. Pure Appl. Math., textbf{56} (2003), 1247–1262.
bibitem{KePoVe}
newblock C. Kenig and G. Ponce and L. Vega,
newblock On the support of solutions to the generalized KdV equation,
newblock Ann. Inst. H. Poincar'e Anal.Non. Lin'earire, textbf{19(2)} (2002), 191–208.
bibitem{Lions}
newblock J. Lions,
newblock Exact controllability, stabilization and perturbations for distributed systems,
newblock SIAM Reviews, textbf{30(1)} (1988), 1–68.
bibitem{Panthee1}
newblock M. Panthee,
newblock Unique continuation property for the Kadomtsev-Petviashvili (KP-II) equation,
newblock Electronic Journal of Differential Equations, textbf{59} (2005), 1–12.
bibitem{Rosenau}
newblock P. Rosenau,
newblock Dynamics of dense discrete systems,
newblock Prog. Theoret. Phys., textbf{79} (1988), 1028–1042.
bibitem{Scheurer}
newblock J. Saut and B. Scheurer,
newblock Unique continuation for some evolution equations,
newblock J. Diff. Equations, textbf{66} (1987), 118–139.
bibitem{YShang}
newblock Y. Shang,
newblock Unique continuation for the symmetric regularized long wave equation,
newblock Mathematical Methods in Applied Sciences, textbf{30} (2007), 375–388.
bibitem{FTre}
newblock F. Treves,
newblock Linear Partial Differential Equations with Constant Coefficients,
newblock Gordon and Breach, N. York, London, Paris, 1966.
bibitem{Cauchy2}
newblock S. Wang and G. Xu,
newblock The Cauchy problem for the Rosenau equation,
newblock Nonlinear Analysis: Theory, Methods and Applications, textbf{71(1)} (2009), 456–466.
bibitem{Zhang-UC}
newblock B. Zhang,
newblock Unique continuation for the Korteweg-de Vries equation,
newblock SIAM J. Anal., textbf{23} (1992), 55–71.