Propagation Property for Nonlinear Parabolic Equations of p-Laplacian-Type

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+ λu = 0, where m, p, q, k > 0, and n-dimensional simplified variant ∂t(u )−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 propagation property. For the second equation we rigorously prove that perturbation of the nonnegative solutions propagates at finite speed if and only if m < p. Mathematics Subject Classification: 35K65, 35K55, 35B20