In this talk, I will introduce the stability of traveling front solutions for a pseudoparabolic Fisher-KPP equation. By applying geometric singular perturbation method, special Evans function estimates, detailed spectral analysis and C0 semigroup theories, all the traveling front solutions with non-critical speeds are proved to be locally exponentially stable in some appropriate exponentially w...

Pseudoparabolic equations in periodic media are homogenized to obtain upscaled limits by asymptotic expansions and two-scale convergence. The limit is characterized and convergence is established in various linear cases for both the classical binary medium model and the highly heterogeneous case. The limit of vanishing time-delay parameter in either medium is included. The double-porosity limit...

We study nonlinear pseudoparabolic equations, on the half-line in a critical case, ∂t(u− uxx)− αuxx = λ|u|u, x ∈ R, t > 0, u(0, x) = u0(x), x ∈ R, u(t, 0) = 0, where α > 0, λ ∈ R. The aim of this paper is to prove the existence of global solutions to the initial-boundary value problem and to find the main term of the asymptotic representation of solutions.

We address the small-time evolution of interfaces (fronts) for the pseudoparabolic generalization ∂u ∂t = ∂ ∂x ( u ∂u ∂x + u ∂2u ∂x∂t ) of the porous-medium equation, identifying regimes in which the local behavior remains fixed for some finite time and others in which it changes instantaneously. A number of phenomena beyond those exhibited by the porous-medium equation are elucidated, includin...