Initial-boundary value problem for the Hirota equation posed on a finite interval

In this paper, we turn our attention to a nonhomogeneous initial boundary value problem for Hirota equation posed on a bounded interval (0,L). In particular, the explicit solution formula of linear nonhomogeneous boundary value problem is established by Laplace transform. Using space L2(0,T;H0s−1(0,...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 526; no. 2; p. 127330
Main Authors Wu, Jun, Guo, Boling
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.10.2023
Subjects
Hirota equation
Initial-boundary value problem
Non-homogeneous boundary
Well-posedness
Non-homogeneous boundary
Hirota equation
Initial-boundary value problem
Well-posedness
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ISSN0022-247X
1096-0813
DOI10.1016/j.jmaa.2023.127330

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Summary:In this paper, we turn our attention to a nonhomogeneous initial boundary value problem for Hirota equation posed on a bounded interval (0,L). In particular, the explicit solution formula of linear nonhomogeneous boundary value problem is established by Laplace transform. Using space L2(0,T;H0s−1(0,1)), which is preparing for trilinear estimates and Lions-Magenes interpolation theorem, we prove the local existence, uniqueness, and Lipschitz continuous in C(0,T;Hs(0,1))∩L2(0,T;Hs+1(0,1)) corresponding to the initial and boundary data. Moreover, the local solution extends to a global one by a priori bound.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2023.127330