Mathematica Bohemica, Vol. 147, No. 2, pp. 237-270, 2022
On a system of nonlinear wave equations with the Kirchhoff-Carrier
and Balakrishnan-Taylor terms
Bui Duc Nam, Nguyen Huu Nhan, Le Thi Phuong Ngoc, Nguyen Thanh Long
Received May 19, 2020. Published online July 8, 2021.
Abstract: 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.
Keywords: system of nonlinear wave equations of Kirchhoff-Carrier type; Balakrishnan-Taylor term; Faedo-Galerkin method; local existence; exponential decay
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Affiliations: Bui Duc Nam, Department of Mathematics and Computer Science, University of Science, 227 Nguyen Van Cu St., Dist. 5, Ho Chi Minh City, Vietnam; Vietnam National University, Ho Chi Minh City, Vietnam, and Ho Chi Minh City University of Food Industry, 140 Le Trong Tan St., Tay Thanh Ward, Tan Phu Dist., Ho Chi Minh City, Vietnam, e-mail: nambd@hufi.edu.vn; Nguyen Huu Nhan, Nguyen Tat Thanh University, 300A Nguyen Tat Thanh St., Dist. 4, Ho Chi Minh City, Vietnam; Department of Mathematics and Computer Science, University of Science, 227 Nguyen Van Cu St., Dist. 5, Ho Chi Minh City, Vietnam, and Vietnam National University, Ho Chi Minh City, Vietnam, e-mail: huunhandn@gmail.com; Le Thi Phuong Ngoc, University of Khanh Hoa, 01 Nguyen Chanh St., Nha Trang City, Vietnam; Department of Mathematics and Computer Science, University of Science, 227 Nguyen Van Cu St., Dist. 5, Ho Chi Minh City, Vietnam, and Vietnam National University, Ho Chi Minh City, Vietnam, e-mail: ngoc1966@gmail.com; Nguyen Thanh Long (corresponding author), Department of Mathematics and Computer Science, University of Science, 227 Nguyen Van Cu St., Dist. 5, Ho Chi Minh City, Vietnam, and Vietnam National University, Ho Chi Minh City, Vietnam, e-mail: longnt2@gmail.com
