Higher order nonlinear degenerate parabolic equations

AbstractThis 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)