Self-similar intermediate asymptotics for a degenerate parabolic filtration-absorption equation

Self-similar intermediate asymptotics for a degenerate parabolic filtration-absorption equation.

The equation partial differential(t)u = u partial differential(xx)(2)u -(c-1)( partial differential(x)u)(2) is known in literature as a qualitative mathematical model of some biological phenomena. Here this equation is derived as a model of the groundwater flow in a water-absorbing fissurized porous rock; therefore, we refer to this equation as a filtration-absorption equation. A family of self...

Self-similar intermediate asymptotics for nonlinear degenerate parabolic free-boundary problems that occur in image processing.

In the boundary layers around the edges of images, basic nonlinear parabolic equations for image intensity used in image processing assume a special degenerate asymptotic form. An asymptotic self-similar solution to this degenerate equation is obtained in an explicit form. The solution reveals a substantially nonlinear effect-the formation of sharp steps at the edges of the images, leading to e...

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

Gradient Estimates for a Degenerate Parabolic Equation with Gradient Absorption and Applications

Qualitative properties of non-negative solutions to a quasilinear degenerate parabolic equation with an absorption term depending solely on the gradient are shown, providing information on the competition between the nonlinear diffusion and the nonlinear absorption. In particular, the limit as t → ∞ of the L1-norm of integrable solutions is identified, together with the rate of expansion of the...

Improved intermediate asymptotics for the heat equation

This letter is devoted to results on intermediate asymptotics for the heat equation. We study the convergence towards a stationary solution in self-similar variables. By assuming the equality of some moments of the initial data and of the stationary solution, we get improved convergence rates using entropy / entropy-production methods. We establish the equivalence of the exponential decay of th...