Question

Consider the diffusion equation on (0, l) with the Robin boundary conditions ux (0, t) − a0u(0, t) = 0 and ux (l, t) + alu(l, t) = 0. If a0 > 0 and al > 0, use the energy method to show that the endpoints contribute to the decrease of l 0 u2(x, t) dx. (This is interpreted to mean that part of the "energy" is lost at the boundary, so we call the boundary conditions "radiating" or "dissipative.")

Answer 1

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