Existence of Solutions of Nonlinear Degenerate Parabolic Problems
by
W. Y. Chan
Department of Mathematics, Southeast Missouri State University
Coauthors: C. Y. Chan (Department of Mathematics, University of Louisiana at Lafayette)

Let T ≤ ∞, r be a nonnegative constant, and m, p and a be positive constants. Existence of a solution for the following nonlinear degenerate parabolic first initial-boundary value problems,
u_t = 1/x^r(x^ru^mu_x)_x+u^p for 0 < x < a and 0 < t < T,
u(x, 0) = u₀(x) for 0 ≤ x ≤ a,
u(0, t) = 0 = u(a, t) for 0 < t < T,
where u₀(x) is a given nonnegative function such that u₀(0) = 0 = u₀(a), is studied.

Date received: March 19, 2007