Propagation Property for Nonlinear Parabolic Equations of p-Laplacian-Type 1
Than Sint Khin, Ning Su · 2009
Abstract. We study propagation property for one-dimensional nonlinear diffusion equations with convection-absorption, including the prototype model ∂t(u m) − ∂x(|∂xu|p−1∂xu) − μ|∂xu|q−1∂xu + λuk = 0, where m, p, q, k> 0, and n-dimensional simplified variant ∂t(u m)−Δp+1u = 0, where Δp+1u = div (|∇u|p−1∇u). Among the conclusions, we make complete classification of the parameters in the first equation to distinguish its propaga-tion property. For the second equation we rigorously prove that perturbation of the nonnegative solutions propagates at finite speed if and only if m < p.