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New Bilinear Estimates for Quadratic-Derivative Nonlinear Wave Equations in 2+1 Dimensions
Bilinear Estimates Quadratic-Derivative Nonlinear
2014/12/8
This thesis is concerned with the Cauchy problem for the quadratic derivative nonlinear wave equation in two spatial dimensions. Using standard techniques, we reduce local well-posedness in Fourier Le...
Adomian decomposition method (ADM) for nonlinear wave-like equations with variable coefficient
Adomian decomposition wave-like equation variable coefficient
2010/9/27
The Adomian Decomposition Method (ADM) has been widely applied in solving partial differential equations which represent various phenomena in engineering and physics. This method is easy to program an...
Asymptotic decay for a one-dimensional nonlinear wave equation
one-dimensional nonlinear wave equation math
2010/11/9
We consider the asymptotic behaviour of finite energy solutions to the one-dimensional defocusing nonlinear wave equation $-u_{tt} + u_{xx} = |u|^{p-1} u$, where $p > 1$. Standard energy methods guar...
The Null Condition and Global Existence for Nonlinear Wave Equations on Slowly Rotating Kerr Spacetimes
Null Condition Global Existence Nonlinear Wave Equations Rotating Kerr Spacetimes
2010/12/16
We study a semilinear equation with derivatives satisfying a null condition on slowly rotating Kerr spacetimes. We prove that given sufficiently small initial data, the solution exists globally in tim...
The Cauchy problem for a class of two-dimensional nonlocal nonlinear wave equations governing anti-plane shear motions in elastic materials
class of two-dimensional nonlocal nonlinear wave equatio elastic materials
2010/12/1
This paper is concerned with the analysis of the Cauchy problem of a general class of two-dimensional nonlinear nonlocal wave equations governing antiplane shear motions in nonlocal elasticity.
Two-point boundary value problems and exact controllability for several kinds of linear and nonlinear wave equations
wave equation two-point boundary value problem global exact controllability exact controllability Dirichlet boundary condition Neumann boundary condition hyperbolic curvature flow Gage-Hamilton’s theorem
2018/4/19
In this paper we introduce some new concepts for second-order hyperbolic equations: two-point boundary value problem, global exact controllability and exact controllability. For several kinds of impor...
Multisymplectic Structure and Multisymplectic Scheme for the Nonlinear Wave Equation
multisymplectic structure multisymplectic schemes
2007/12/11
The multisymplectic structure of the nonlinear wave wquation is derived directly from the variational principle. In the numerical aspect, we present a multisymplectic nine points scheme which is equiv...