Suppose we have ut = a²uₓₓ, 0 < x < 1,t > 0, boundary conditions are u(0,t) = u(1,t) = 0, and the initial condition is u(x,0) = sin(1x). What will be the behavior of u(x, t) as time increases. There may be more than one correct answer. You do not need to solve the equation to answer this question.
A. The solution behaves unpredictably.
B. For a fixed t, the solution will look kind of like an inverted parabola.
C. The solution increases to infinity.
D. For a fixed t, the second x derivative, Uzz, will take on both signs.
E. The solution increases slowly towards u = 0.
F. For a fixed t, the solution will be linear
G. For a fixed t, the second x derivative, Uzt, will always be negative.
H. The solution decreases slowly towards u = 0.
I. The solution decreases to minus infinity.
J. The solution does not change as time goes on.
K. None of the above
