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5 results on '"Bui, Duc Nam"'

1. On a system of nonlinear wave equations with the Kirchhoff-Carrier and Balakrishnan-Taylor terms

Author

Bui Duc Nam, Nguyen Huu Nhan, Le Thi Phuong Ngoc, and Nguyen Thanh Long

Subjects
system of nonlinear wave equations of kirchhoff-carrier type, balakrishnan-taylor term, faedo-galerkin method, local existence, exponential decay, Mathematics, QA1-939
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.

Published
2022
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2. Regularity and convergent result of mild solution of Love equation.

Author

Bui, Duc Nam, Nghia, Bui Dai, and Phuong, Nguyen Duc

Subjects
EQUATIONS, HILBERT space
Abstract

In this paper, we are interested to study a mild solution of the Love equation. This type of equation has many applications in physics. Under various assumptions of the Cauchy data, we obtain the regularity of the mild solution. We also obtain the continuity of the mild solution concerning the parameter. We show that the mild solution of the Love equation converges to the mild solution of the wave equation. Our work may be the first paper on the mild solution of the Love equation. [ABSTRACT FROM AUTHOR]

Published
2024
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4. Existence and exponential decay of the Dirichlet problem for a nonlinear wave equation with the Balakrishnan–Taylor term*

Author

Nguyen Thanh Long, Bui Duc Nam, Le Thi Phuong Ngoc, and Nguyen Huu Nhan

Subjects
Dirichlet problem, General Mathematics, 010102 general mathematics, 01 natural sciences, Exponential function, Term (time), 010104 statistics & probability, Number theory, Linearization, Ordinary differential equation, Applied mathematics, 0101 mathematics, Exponential decay, Energy (signal processing), Mathematics
Abstract

In this paper, we consider the Dirichlet problem for a nonlinear wave equation with Balakrishnan–Taylor term. We establish the local existence is established by the linearization method together with the Faedo–Galerkin method. Next, we prove an exponential energy decay result by suitable Lyapunov functionals.

Published
2020
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5. High-Order Iterative Scheme for a Viscoelastic Wave Equation and Numerical Results

Author

Nguyen Huu Nhan, Doan Thi Nhu Quynh, Tran Trinh Manh Dung, Le Thi Mai Thanh, and Bui Duc Nam

Subjects
Scheme (programming language), Sequence, Article Subject, Iterative method, 020209 energy, General Mathematics, Weak solution, 010102 general mathematics, General Engineering, 02 engineering and technology, Wave equation, Engineering (General). Civil engineering (General), 01 natural sciences, Viscoelasticity, 0202 electrical engineering, electronic engineering, information engineering, QA1-939, Order (group theory), Applied mathematics, 0101 mathematics, TA1-2040, Galerkin method, computer, Mathematics, computer.programming_language
Abstract

In this paper, we consider a Robin problem for a viscoelastic wave equation. First, by the high-order iterative method coupled with the Galerkin method, the existence of a recurrent sequence via an N -order iterative scheme is established, and then the N -order convergent rate of the obtained sequence to the unique weak solution of the proposed model is also proved. Next, with N = 2 , a numerical algorithm given by the finite-difference method is constructed to approximate the solution via the 2-order iterative scheme. Moreover, the same algorithm for the single-iterative scheme generated by the 2-order iterative scheme is also considered. Finally, comparison with errors of the numerical solutions obtained by the single-iterative scheme and the 2-order iterative scheme shows that the convergent rate of the 2-order iterative scheme is faster than that of the single-iterative scheme.

Published
2021

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