• Kyungpook Mathematical Journal
• /
• v.59 no.4
• /
• pp.631-649
• /
• 2019

In this paper, we prove the global nonexistence of solutions for a quasilinear wave equation with time delay and acoustic boundary conditions. Further, we establish the blow up result under suitable conditions.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.3
• /
• pp.811-821
• /
• 2013

We study the initial value problem of the exponential wave equation in $\math{R}^{n+1}$ for small initial data. We shows, in the case of $n=1$, the global existence of solution by applying the formulation of first order quasilinear hyperbolic system which is weakly linearly degenerate. When $n{\geq}2$, a vector field method is applied to show the stability of a trivial solution ${\phi}=0$.

• Journal of the Korean Mathematical Society
• /
• v.48 no.4
• /
• pp.867-885
• /
• 2011

We study a class of quasilinear wave equations with strong and nonlinear viscosity. By using the perturbation method for semilinear parabolic equations, we have established the fundamental results on existence, uniqueness and continuous dependence on data of weak solutions.

• Journal of the Korean Mathematical Society
• /
• v.37 no.3
• /
• pp.339-358
• /
• 2000

Let be a bonded domain in N with smooth boundary . In this paper, we consider the existence of solutions of the following problem: (1.1)-div{} - + = , , , , , , where q > 1, p$\geq$1, $\delta$>0, , the Laplacian in N and is a positive function like as .

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.2
• /
• pp.245-252
• /
• 2006

In this paper we study the uniform decay estimates of the energy for the nonlinear wave equation of Kirchhoff type $$y'(t)-M({\mid}{\nabla}y(t){\mid}^2){\triangle}y(t)\;+\;{\delta}y'(t)=f(t)$$ with the damping constant ${\delta} > 0$ in a bounded domain ${\Omega}\;{\subset}\;\mathbb{R}^n$.

• Journal of the Korean Society for Nondestructive Testing
• /
• v.36 no.2
• /
• pp.102-111
• /
• 2016

This study develops an efficient and accurate method for calculating nonlinear diffraction beam fields propagating in fluids or solids. The Westervelt equation and quasilinear theory, from which the integral solutions for the fundamental and second harmonics can be obtained, are first considered. A computationally efficient method is then developed using a multi-Gaussian beam (MGB) model that easily separates the diffraction effects from the plane wave solution. The MGB models provide accurate beam fields when compared with the integral solutions for a number of transmitter-receiver geometries. These models can also serve as fast, powerful modeling tools for many nonlinear acoustics applications, especially in making diffraction corrections for the nonlinearity parameter determination, because of their computational efficiency and accuracy.