Let k, L > 0 and suppose u(x, t) satisfies the Dirichlet problem u(x, 0) =...

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Let k, L > 0 and suppose u(x, t) satisfies the Dirichlet problem u(x, 0) = 0, u(0, t) = u(L, t) = 0, ut - kurr - sin u, where 0 < x < L and t 0. Show that there exists a constant C> 0 such that for all 0 Let k, L > 0 and suppose u(x, t) satisfies the Dirichlet problem u(x, 0) = 0, u(0, t) = u(L, t) = 0, ut - kurr - sin u, where 0 < x < L and t 0. Show that there exists a constant C> 0 such that for all 0