MATH 19A Midterm: MATH19 Harvard Midterm2F02sol19 Fall 04
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Advection. (b) the distribution of a certain protein in a cell after the protein has reached a steady-state. Laplace. (c) the spread of airborne radioactivity after chernobyl disaster in 1986. Advection. (d) the spread of the oil spill from the exxon valdez in prince william. Advection. (e) the spread of killer bees when they rst escaped from captivity in. X2 . (1) (15 points) (a) verify that u(t, x) = e t sin x is a solution to (1). X2 e t sin x = e t 2. Therefore, u(t, x) = e t sin x is a solution to (1). (b) verify that u(t, x) = e 4t sin 2x is a solution to (1). Di erentiating u with respect to t, we get. On the other hand, di erentiating u with respect to x, we get. X2 e 4t sin 2x = e 4t 2.
