Unique Continuation for the Kawahara Equation
DOI:
https://doi.org/10.5540/tema.2007.08.03.0463Abstract
We establish a unique continuation property for the Kawahara equation. To state such property, we use a Carleman inequality for a linear differential operator related to the Kawahara equation.References
[1] T.B. Benjamin, J.L. Bona, J.J. Mahony, Model equations for long waves in nonlinear dispersive systems, Philos. Trans. Roy. Soc. London, Ser. A 272 (1972), 47-78.
H.A. Biagioni, F. Linares, On the Benney-Lin and Kawahara equations, J. Math. Anal. Appl., 211 (1997), 131-152.
C.E. Kenig, “Some Recent Quantitative Unique Continuation Theorems”, Notes of the Lecture on the Prairie Analysis Seminar, DM, Kansas State University (2005).
G.P. Menzala, C.F. Vasconcellos, E. Zuazua, Stabilization of the Kortweg-de Vries equation with localized damping, Quarterly of Applied Mathematics, 60, No. 1 (2002), 111-129.
L. Rosier, Exact controllability for the Korteweg-De Vries equation on a bounded domain, Control Optmization and Calculus of Variations, 2 (1997), 33-55.
J.C. Saut, B. Scheurer, Unique continuation for some evolution equations, Diff. Equations, 66 (1987), 118-139.
Y. Shang, Unique continuation for symmetric regularized long wave equation, Research Report of The Institute of Mathematical Sciences of The Chinese University of Hong Kong, Shatin, Hong Kong, 125 (2005).
C.F. Vasconcellos, Exact controllability for the Korteweg-De Vries-Kawahara equation on a bounded domain, X ICCAM, K. U. Leuven (2002).
B.-Y. Zhang, Unique continuation for the Kortweg-de Vries equation, SIAM J. Math. Anal., 23 (1991), 55-71.
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