PDE Wave Equation and Energy Conservation

[Maybe_Memorie]

Homework Statement

Just looking back through my notes and it looks like I'm missing some. Just a few questions.

For one example in the notes I have the wave u_tt-c²u_xx + u³ = 0 and that the energy density 1/2u²_t + c²/2u²_x + 1/4u⁴

I have that the differential form of energy conservation is ε_t = μ_x + (wave equation)μ_t = μ_x for solutions.

First question, what is the integral form of energy conservation?

The notes then say that here μ = c²u_tu_x. Why is this?

Also what is the difference between global and local form of energy conservation? Is it just that local has finite limits?

Are there any websites or online notes that might have some of this info? I searched a lot but can't find much

Thanks!

 

[I like Serena]

Hey Maybe_Memorie!

I think that before we can give an answer, we first need some definitions.
What does each of your symbols represent?
And what do they mean?
To be honest, I felt a bit reluctant to respond, since I have no idea what I'm getting into with these fragments of information.

Btw, are you still 17? (Your blog says so. )