Existence and Uniqueness of a Blow-up Solution in Sense of Semigroup Theory of a Degenerate Semilinear Parabolic Problem

摘要

We prove under appropriate assumptions the existence and uniqueness in the sense of semigroup theory of a blow-up solution for a degenerate semilinear parabolic problem: ut - (a(x)u_x)_x = f(u) in (0,1) × (0, ∞) where f is a given function and a(0) = 0, a(x) > 0 on (0,1) together with the Dirichlet boundary condition and the suitable initial condition.