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ABSTRACT. This paper establishes conditions for the differentiability of solutions to mixed problems for first order hyperbolic systems of the form (3/3» -2 Aja/dxj -B)u = F on [0, r] X ß, Mu -g on [0,7"] x 3Í2, u(0, x) -f(x), x e Q. Assuming that X1 a priori inequalities are known for this equation, it is shown that if F e H'([0, T] x Q), g e H'*l'2([0, T] X 3ñ),/ e H'(Q) satisfy the natural compatibility conditions associated with this equation, then the solution is of class C from [0, T] to H'~f(Q), 0 < p < s. These results are applied to mixed problems with distribution initial data and to quasi-linear mixed problems.

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Two never-smoking cohorts in Southern California, one in Lancaster (N = 2340) exposed only to moderate levels of oxidants and the other in Long Beach (N = 1326) exposed to high levels of SOx, NO2, hydrocarbons and particulates completed spirometry and the single-breath nitrogen test five to six years apart. Forty-seven percent and 45 percent of the participants were retested. Mean results at baseline for those tested and not retested were similar. Loss to follow-up was primarily due to moving (39 percent and 47 percent). Every difference of consequence indicated greater deterioration in lung function in Long Beach. The level of significance of the difference was greatest, even in the youngest age groups, for delta N2(750-1250), suggesting that the earliest site of impairment may occur in the small airways. Greater deterioration in spirometric parameters was observed in every age group in Long Beach females above seven years of age at baseline and in Long Beach males above 15 years of age, suggesting that chronic exposure to the pollutant mix occurring in Long Beach ultimately adversely affects the large airways as well as small airways.