# PDE and conservation of energy

#### Markov

##### Member
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?

#### dwsmith

##### Well-known member
Can anybody help please?
I suggested a cheap good book for you to get but you decided against it. Why didn't you buy a something (a book on the matter) that can help you start the problem?

#### Markov

##### Member
Yes but I can't get that book.