(a)
Chapter 4, Problem 4.3.11(choose chapter or problem)
(a) Provethatthe(total)energyisconservedforthewaveequationwith Dirichlet BCs, where the energy is dened to be E = 1 2 l 0 c2u2 t +u2 xdx.(Compare this denition with Section 2.2.) (b) Do the same for the Neumann BCs. (c) For the Robin BCs, show that ER = 1 2 l 0 c2u2 t +u2 xdx+ 1 2al[u(l,t)]2 + 1 2a0[u(0,t)]2 is conserved. Thus, while the total energy ER is still a constant, someoftheinternalenergyislosttotheboundaryifa0 andal are positive and gained from the boundary if a0 and al are negative
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