Geodesic
Asymptotic expansion of solutions for the Robin-Dirichlet problem of Kirchhoff-carrier type with Balakrishnan-Taylor damping
Filomat, Tome 37 (2023) no. 8, p. 2321

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In this paper, we consider the Robin-Dirichlet problem for a nonlinear wave equation of Kirchhoff-Carrier type with Balakrishnan-Taylor damping. First, under suitable conditions on the initial data, the local existence and uniqueness of a weak solution are proved. Next, an asymptotic expansion of solutions in a small parameter with high order is established. The used main tools are the linearization method for nonlinear terms together with the Faedo-Galerkin method, and the key lemmas of the expansion of high-order polynomials and the Taylor expansion for multi-variable functions.
DOI : 10.2298/FIL2308321N
Classification : 35L20, 35L70, 35Q74, 37B25
Keywords: Nonlinear wave equation, Balakrishnan-Taylor damping, Faedo-Galerkin method, Local existence, Asymptotic expansion 
Nguyen Huu Nhan; Bui Duc Nam; Le Thi Phuong Ngoc; Nguyen Thanh Long. Asymptotic expansion of solutions for the Robin-Dirichlet problem of Kirchhoff-carrier type with Balakrishnan-Taylor damping. Filomat, Tome 37 (2023) no. 8, p. 2321 . doi: 10.2298/FIL2308321N
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     title = {Asymptotic expansion of solutions for the {Robin-Dirichlet} problem of {Kirchhoff-carrier} type with {Balakrishnan-Taylor} damping},
     journal = {Filomat},
     pages = {2321 },
     year = {2023},
     volume = {37},
     number = {8},
     doi = {10.2298/FIL2308321N},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2308321N/}
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