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This is the part of the proof for the finite speed of propagation of wave equation that i am learning. I am not understanding how the boundary term come in the first step ie while finding $\dot e(t)$ . Next doubt is after integrating by parts the first term becomes zero , why is it so ? is it because $u_{tt}-\Delta u =0$ or is it because of the conditions given ie $u_t=0$ Thanks in advance.

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