- Partial Differential Equations Graduate 1 (61.37 KiB) Viewed 33 times
partial differential equations (graduate)
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partial differential equations (graduate)
partial differential equations (graduate)
Q2) Let u be a smooth solution of the wave equation, which is L- periodic with respect to the space variable, that is u is a solution of the problem UttUxx=0, x ER, t > 0, - under the condition u(x, t) = u(x + L, t), x = R, t> 0. Show that 1 [⁄u²(x, t) + —⁄u²(x, t) + 3⁄u²(x, t)u²(x, t)]dx is constant.
Q2) Let u be a smooth solution of the wave equation, which is L- periodic with respect to the space variable, that is u is a solution of the problem UttUxx=0, x ER, t > 0, - under the condition u(x, t) = u(x + L, t), x = R, t> 0. Show that 1 [⁄u²(x, t) + —⁄u²(x, t) + 3⁄u²(x, t)u²(x, t)]dx is constant.
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