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A wave equation associated with mixed nonhomogeneous conditions: The compactness and connectivity of weak solution set.

Long, Nguyen Thanh; Ngoc, Le Thi Phuong — 2007

Abstract and Applied Analysis

On a fixed point theorem of Krasnosel'skii type and application to integral equations.

Ngoc, Le Thi Phuong; Long, Nguyen Thanh — 2006

Fixed Point Theory and Applications [electronic only]

Positive solutions for an m-point boundary-value problem.

Truong, Le Xuan; Ngoc, Le Thi Phuong; Long, Nguyen Thanh — 2008

Electronic Journal of Differential Equations (EJDE) [electronic only]

Boundary and initial value problems for second-order neutral functional differential equations.

Le, Hoan Hoa; Le, Thi Phuong Ngoc — 2006

Electronic Journal of Differential Equations (EJDE) [electronic only]

On a high-order iterative scheme for a nonlinear Love equation

Le Thi Phuong Ngoc; Nguyen Tuan Duy; Nguyen Thanh Long — 2015

Applications of Mathematics

In this paper, a high-order iterative scheme is established for a nonlinear Love equation associated with homogeneous Dirichlet boundary conditions. This is a development based on recent results (L. T. P. Ngoc, N. T. Long (2011); L. X. Truong, L. T. P. Ngoc, N. T. Long (2009)) to get a convergent sequence at a rate of order $N \geq 2$ to a local unique weak solution of the above mentioned equation.

Existence, blow-up and exponential decay for a nonlinear Love equation associated with Dirichlet conditions

Le Thi Phuong Ngoc; Nguyen Thanh Long — 2016

Applications of Mathematics

In this paper we consider a nonlinear Love equation associated with Dirichlet conditions. First, under suitable conditions, the existence of a unique local weak solution is proved. Next, a blow up result for solutions with negative initial energy is also established. Finally, a sufficient condition guaranteeing the global existence and exponential decay of weak solutions is given. The proofs are based on the linearization method, the Galerkin method associated with a priori estimates, weak convergence,...

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 — 2022

Mathematica Bohemica

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.

On a Kirchhoff-Carrier equation with nonlinear terms containing a finite number of unknown values

Nguyen Vu Dzung; Le Thi Phuong Ngoc; Nguyen Huu Nhan; Nguyen Thanh Long — 2024

Mathematica Bohemica

We consider problem (P) of Kirchhoff-Carrier type with nonlinear terms containing a finite number of unknown values $u (η_{1}, t), \dots, u (η_{q}, t)$ with $0 \leq η_{1} < η_{2} < \dots < η_{q} < 1 .$ By applying the linearization method together with the Faedo-Galerkin method and the weak compact method, we first prove the existence and uniqueness of a local weak solution of problem (P). Next, we consider a specific case $(P_{q})$ of (P) in which the nonlinear term contains the sum $S_{q} [u^{2}] (t) = q^{- 1} \sum_{i = 1}^{q} u^{2} (\frac{(i - 1)}{q}, t)$ . Under suitable conditions, we prove that the solution of $(P_{q})$ converges to the solution of the corresponding...

Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term

Doan Thi Nhu Quynh; Nguyen Huu Nhan; Le Thi Phuong Ngoc; Nguyen Thanh Long — 2023

Applications of Mathematics

We study existence, uniqueness, continuous dependence, general decay of solutions of an initial boundary value problem for a viscoelastic wave equation with strong damping and nonlinear memory term. At first, we state and prove a theorem involving local existence and uniqueness of a weak solution. Next, we establish a sufficient condition to get an estimate of the continuous dependence of the solution with respect to the kernel function and the nonlinear terms. Finally, under suitable conditions...

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Currently displaying 1 – 9 of 9

A wave equation associated with mixed nonhomogeneous conditions: The compactness and connectivity of weak solution set.

On a fixed point theorem of Krasnosel'skii type and application to integral equations.

Positive solutions for an m-point boundary-value problem.

Boundary and initial value problems for second-order neutral functional differential equations.

On a high-order iterative scheme for a nonlinear Love equation

Existence, blow-up and exponential decay for a nonlinear Love equation associated with Dirichlet conditions

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

On a Kirchhoff-Carrier equation with nonlinear terms containing a finite number of unknown values

Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term