LAUSR

For a class of semilinear parabolic equations with discontinuous coefficients, the strong solvability of the Dirichlet problem is studied in this paper. 'e problem ????ni,j�1 aij(t, x)uxixj − ut + g(t, x, u) � f(t, x), u|Γ(QT) � 0, in QT � Ω × (0, T) is the subject of our study, where Ω is bounded C2 or a convex subdomain of En+1, Γ(QT) � zQT\ t � T { }. 'e function g(x, u) is assumed to be a Caratheodory function satisfying the growth condition |g(t, x, u)|≤ b0|u| , for b0 > 0, q ∈ (0, (n + 1)/(n − 1)), n≥ 2, and leading coefficients satisfy Cordes condition b0 > 0, q ∈ (0, (n + 1)/(n − 1)), n≥ 2.