Geodesic
On a system of nonlinear wave equations with the Kirchhoff-Carrier and Balakrishnan-Taylor terms
Mathematica Bohemica, Tome 147 (2022) no. 2, pp. 237-270

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We study a system of nonlinear wave equations of the Kirchhoff-Carrier type containing a variant of the Balakrishnan-Taylor damping in nonlinear terms. By the linearization method together with the Faedo-Galerkin method, we prove the local existence and uniqueness of a weak solution. On the other hand, by constructing a suitable Lyapunov functional, a sufficient condition is also established to obtain the exponential decay of weak solutions.
DOI : 10.21136/MB.2021.0094-20
Classification : 35L20, 35L70, 35Q74, 37B25
Keywords: system of nonlinear wave equations of Kirchhoff-Carrier type; Balakrishnan-Taylor term; Faedo-Galerkin method; local existence; exponential decay 
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Nam, Bui Duc; Nhan, Nguyen Huu; Ngoc, Le Thi Phuong; Long, Nguyen Thanh. On a system of nonlinear wave equations with the Kirchhoff-Carrier and Balakrishnan-Taylor terms. Mathematica Bohemica, Tome 147 (2022) no. 2, pp. 237-270. doi: 10.21136/MB.2021.0094-20

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