Question: (4 points) (a) For given D > 0 and a, c E R, consider the equation ut = Durr + cur - au for x

(4 points) (a) For given D > 0 and a, c E R, consider the equation ut = Durr + cur - au for x E R and t > 0. Assume that u(x, t) is a solution of this equation. Verify that v(y, t) := u(y - ct, t)eat is a solution of Ut = Dvyy for y E R and t > 0. v(y, t) = e - y2 / ( 4t ) VArt satisfies Ut = Vyy for y E R and t > 0. Use the preceding part to find the solution u(x, t) to ut = Uxx + 2ux - 0.5u

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