HIGHER-ORDER NONLINEAR DEGENERATE PARABOLIC EQUATIONS

This paper is concerned with nonlinear degenerate parabolic equations of the form ut + (-1)m - 1 D(f(u) D2m + 1u) = 0 with f(u) ~ |u|n (n ≥ 1) near u = 0 and D = ∂ ∂x. Under appropriate boundary conditions it is shown that there exists a weak solution u. Some of the main results of the paper are that u ≥ 0 if u0 ≥ 0, and that the support of u(·, t) (when u0 ≥ 0) increases with t (for the last property we require that n ≥ 2 and m = 1). © 1990.