Lower regularity solutions of the non-homogeneous boundary-value problem for a higher order Boussinesq equation in a quarter plane. (August 2022)

• Record Type: Journal Article
• Authors: Li, Shenghao; Chen, Min; Yang, Xin; Zhang, Bing-Yu
• Is Part Of: Nonlinear analysis. Volume 221(2022)
• Publication Date: 2022-08
• Subjects: 35Q53 -- 35Q55 -- 35Q35; Boundary value problem -- Bourgain space -- Sixth order Boussinesq equation; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.112893
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We continue to study the initial–boundary-value problem of the sixth order Boussinesq equation in a quarter plane with non-homogeneous boundary conditions: u t t − u x x + β u x x x x − u x x x x x x + ( u 2 ) x x = 0, x, t ∈ R +, u ( x, 0 ) = φ ( x ), u t ( x, 0 ) = ψ ′ ′ ( x ), u ( 0, t ) = h 1 ( t ), u x x ( 0, t ) = h 2 ( t ), u x x x x ( 0, t ) = h 3 ( t ), where β = ± 1 . We show that the problem is locally analytically well-posed in the space H s ( R + ) for any s > − 3 4 with the initial-value data ( φ, ψ ) ∈ H s ( R + ) × H s − 1 ( R + ) and the boundary-value data ( h 1, h 2, h 3 ) ∈ H s + 1 3 ( R + ) × H s − 1 3 ( R + ) × H s − 3 3 ( R + ) .