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Periodic and almost periodic solutions for the damped Korteweg‐de Vries equation
Author(s) -
Chen Mo
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5218
Subject(s) - korteweg–de vries equation , mathematics , uniqueness , bounded function , mathematical analysis , domain (mathematical analysis) , dispersionless equation , kadomtsev–petviashvili equation , partial differential equation , nonlinear system , physics , characteristic equation , quantum mechanics
The Korteweg‐de Vries equation is an important model for propagation of some surface water waves along a channel. In this paper, we discuss the damped Korteweg‐de Vries equation in a bounded domain. First, we study the existence and uniqueness of the strong solution. Then, we prove that the strong solution is periodic (or almost periodic) if the coefficient and external force are periodic (or almost periodic).