Reaction-diffusion in irregular domains

We consider the Cauchy-Dirichlet and Dirichlet problems for the nonlinear parabolic equation u(t) - a(u(m))(xx) + bu(beta) = 0, where a > 0, b is an element of R(1), m > 0, and beta > 0. The problems are considered in noncylindrical domains with nonsmooth boundaries. Existence, uniqueness, and comparison results are established. Constructed solutions are continuous up to the nonsmooth boundary if at each interior point the left modulus of the lower (respectively upper) semicontinuity of the left (respectively right) boundary curve satisfies an upper The (respectively lower) Holder condition neat zero with Holder exponent v > 1/2. value 1/2 is critical as in the classical theory of the heat equation u(t) = u(xx). (C) 2000 Academic Press.