- #1
Markov2
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- 0
Let $u\in\mathcal C^1(\overline R)\cap \mathcal C^2(R)$ where $R=(0,1)\times(0,\infty).$ Suppose that $u(x,t)$ verifies the following wave equation $u_{tt}=K^2 u_{xx}+h(x,t,u)$ where $K>0$ and $h$ is a constant function.
a) Determine the total energy of the string. (Well I don't know what does this mean.)
b) Show that if homogenous boundary conditions are imposed and no extern forces apply to the system, then there's conservation of the energy.
How do I start?
a) Determine the total energy of the string. (Well I don't know what does this mean.)
b) Show that if homogenous boundary conditions are imposed and no extern forces apply to the system, then there's conservation of the energy.
How do I start?
