Carleman estimates and unique continuation property for the Kadomtsev–Petviashvili equations

References

• Kadomtsev , BB and Petviashvili , VI . 1970 . Model equation for long waves in nonlinear dispersive systems . Sov. Phys. Doklady , 15 : 891 – 907 .
   Google Scholar
• Benjamin , TB , Bona , JL and Mahony , JJ . 1972 . Model equations for long waves in nonlinear dispersive systems . Philos. Trans. R. Soc. Lond. Ser. A , 272 ( 1220 ) : 47 – 78 .
   Web of Science ®Google Scholar
• Mammeri , Y . 2007 . Comparaison entre modèles d'ondes de surface en dimension 2 . M2AN Math. Model. Numer. Anal. , 41 ( 3 ) : 513 – 542 .
   Google Scholar
• Carleman , T . 1933 . Sur les systemes linaires aux drives partielles du premier ordre a deux variables . C. R. Acad. Sci. Paris , 197 : 471 – 474 .
   Google Scholar
• Saut , J-C and Scheurer , B . 1987 . Unique continuation for some evolution equations . J. Differ. Eqns , 66 : 118 – 139 .
   Web of Science ®Google Scholar
• Bourgain , J . 1997 . On the compactness of the support of solutions of dispersive equations . Int. Math. Res. Notices , 9 : 437 – 447 .
   Google Scholar
• Panthee , M . 2005 . Unique continuation property for the Kadomtsev-Petviashvili (KP-II) equation . Electron. J. Differ. Eqns , 2005 ( 59 ) : 1 – 12 .
   Google Scholar
• Constantin , A . 2005 . Finite propagation speed for the Camassa-Holm equation . J. Math. Phys. , 46 023506, pp. 1–4
   Web of Science ®Google Scholar
• Mammeri , Y . 2009 . Unique continuation property for the KP-BBM-ii equation . Diff. Integral Eqns , 22 ( 3–4 ) : 393 – 399 .
   Web of Science ®Google Scholar
• Davila , M and Menzala , GP . 1998 . Unique continuation for the Benjamin-Bona-Mahony and Boussinesq's equations . Nonlinear Differ. Eqns Appl. , 5 : 367 – 382 .
   Google Scholar
• Saut , J-C and Tzvetkov , N . 2004 . Global well-posedness for the KP-BBM equations . AMRX Appl. Math. Res. Express , 1 : 1 – 16 .
   Google Scholar
• Treves , F . 1966 . Linear Partial Differential Equations with Constant Coefficients , New York, London , , Paris : Gordon & Breach .
   Google Scholar
• Nirenberg , L . 1957 . Uniqueness of Cauchy problems for differential equations with constant leading coefficient . Commun. Pure Appl. Math. , 10 : 89 – 105 .
   Web of Science ®Google Scholar
• Iório , RJ Jr and Nunes , WVL . 1998 . On equations of KP-type . Proc. R. Soc. Edinb. Sect. A , 128 ( 4 ) : 725 – 743 .
   Google Scholar
• Bourgain , J . 1993 . On the Cauchy problem for the Kadomtsev-Petviashvili equation . Geom. Funct. Anal. , 3 ( 4 ) : 315 – 341 .
   Google Scholar