On the unique continuation property of solutions of the\n three-dimensional Zakharov-Kuznetsov equation

2017/02/08 by Eddye Bustamante, Bustamante, Eddye, José Jiménez Urrea +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Waves and Solitons #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1702.02610

openalex publication_date 2017/02/08 · openalex created_date 2022/09/17 · openalex updated_date 2026/07/28

Abstract

We prove that if the difference of two sufficiently smooth solutions of the\nthree-dimensional Zakharov-Kuznetsov equation\n
partial_tu+
partial_x
triangle u+u
partial_xu=0
text,
quad\n(x,y,z)
in
mathbb R³,
;t
in[0,1], decays as e^-a(x²+y²+z²)^3/4 at\ntwo different times, for some a>0 large enough, then both solutions coincide.\n

Citations

• On the generalized Zakharov-Kuznetsov equation at critical regularity

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