Wave Equation Solution by Factoring Operators
2011年11月21日 · Notice that the wave equation's partial derivatives below are factored into first order PDE operators like a second degree polynomial. Then, these PDE operators are applied one at a time to get the wave equation for u.
Show that the wave equation does not satisfy the maximum …
2015年9月9日 · But in diffusion equation, we have as boundary the square delimited by $[0,L]\times[0,T]$. If we need to define something like this for the wave equation, the maximum will be at a square side and I don't know what to do.
Method of reflections for the wave equation.
2015年6月11日 · For the Wave Equation: $ \left\{\begin{matrix} u_{tt}-c^2u_{xx}=0 & x>0, t>0\\ u(x,0)=f(x) & x>0 & \hspace{0.5cm} (1) \\ u_{t}(x,0)=g(x) & x>0 & \hspace{0.5cm} (1 ...
Solving the wave equation with Neumann conditions
1D Wave Equation with Coupled IC's and Non-Homogeneous BC's. Hot Network Questions
Uniqueness of solutions to the wave equation
2015年1月21日 · Uniqueness to the wave equation in $\mathbb R^n$ using the energy method. 0. Wave equation and Energy. 0.
Why is the wave equation second order - Mathematics Stack …
2015年7月18日 · One can prove that the wave equation is the simplest equation among all which satisfy those invariance properties. $\endgroup$ – Mariano Suárez-Álvarez Commented Jul 18, 2015 at 6:17
Robin BC in the 1D wave equation - Mathematics Stack Exchange
2019年3月14日 · $\begingroup$ @pluton, to be precise, the boundary condition you are considering, strictly speaking, is not the standard Robin condition: this has the following form $$\left[\partial_x u(x,t)+\alpha u(x,t)\right]_{x=0}=0 \iff \partial_x u(0,t)=\color{red}{-\alpha} u(0,t).$$ In this form, the condition $\alpha>0$ implies existence and uniqueness of a solution for the …
Wave Equation From Cartesian Coordinates to Polar Coordinates ...
Now we can see that the wave equation $\Delta u(x,y,t)=\frac{1}{c^2}\partial_t^2u(x,y,t) ...
Is the wave equation a hyperbolic, parabolic, or elliptic PDE?
2022年9月9日 · $\begingroup$ Yes, it is hyperbolic. If you think of $\partial/\partial x=X$ and $\partial/\partial t=T$, the equation looks like $(X^2-T^2)u=0$, and this looks like the equation of a hyperbola.
2D wave equation: decay estimate - Mathematics Stack Exchange
2015年5月28日 · Wave equation with Neumann BC on semi-infinite domain. 1. Explicit solution of wave equation in 3D using ...