Let u be the unique solution of where (x, t) e (0, 1) x (0, 00),u(x, 0) = at ax? sin Tx, x e (0, 1) u(0, t) = u(1, t) = 0t e (0, 0) Then which of the following are true? %3D (a) 3 (x, t) e (0, 1) x (0, 0) s.t. u(x, t) = 0 (b) 3 (х, t) € (0, 1) x (0, оо) s.t. ди (x,1) D0 (c) The function e'u(x, t) is bounded for (x, t) e (0, 1) x (0, 0) (d) 3 (x, t) e (0, 1) x(0, 0) s.t. u(x, t) > 1

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