now the product formula_9 occurring in the pde seems to be undefined, since the distribution "m" is supported at the very point where the derivative "u" is undefined. an ad hoc interpretation is to take the value of "u" at that point to equal the average of its left and right limits (zero, in this case). a more satisfactory way to make sense of the solution is to invert the relationship between "u" and "m" by writing formula_10, where formula_11, and use this to rewrite the pde as a (nonlocal) hyperbolic conservation law: