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PDE and conservation of energy

Markov

Member
Feb 1, 2012
149
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
Feb 1, 2012
1,673
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
Feb 1, 2012
149
Yes but I can't get that book. :(