Correct answer: (B) u(x,t)=u(1−x,t).; (C) ∫₀¹u² dx decreases with t.
Explanation
Initial maximum is 1/2 at x=1/2, refuting A. Initial data and boundaries are reflection symmetric; uniqueness proves B. Integration by parts yields $d\int u^2dx/dt=4\int uu_{xx}dx=-4\int u_x^2dx<0$ for the nonzero solution, proving C and refuting D. **B,C**.
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