MHB Does the Wave Equation with Homogeneous Boundary Conditions Conserve Energy?

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The discussion centers on the wave equation with homogeneous boundary conditions and its implications for energy conservation. It begins with a request for guidance on determining the total energy of a string described by the wave equation. Participants emphasize that under homogeneous boundary conditions and in the absence of external forces, energy is conserved in the system. There is also a suggestion for acquiring a book to aid in understanding the topic, but the original poster expresses difficulty in obtaining it. Overall, the conversation highlights the importance of foundational resources in tackling complex mathematical problems.
Markov2
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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?
 
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Markov said:
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?
 
Yes but I can't get that book. :(
 

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