We consider a fully practical nite element approximation of the fourth order nonlinear degenerate parabolic equation u t + r:(b(u)ru)= 0; where generically b(u) := juj p for any given p 2 (0; 1). An iterative scheme for solving the resulting nonlinear discrete system is analysed. In addition to showing well-posedness of our approximation, we prove convergence in one space dimension. Finally som...

This paper studies the averaging problem for some fully nonlinear equations of degenerate parabolic type with a Hamiltonian not necessarily periodic in the fast variable. Our aim is to point out a sufficient condition on the Hamiltonian to pass to the limit in the starting equation. Also, we investigate when this condition is not completely fulfilled and discuss some examples concerning determi...

The purpose of this work is to deal with the blow-up behavior of the nonnegative solution to a degenerate and singular parabolic equation with nonlocal boundary condition. The conditions on the existence and non-existence of the global solution are given. Further, under some suitable hypotheses, we discuss the blow-up set and the uniform blow-up profile of the blow-up solution. c ©2016 All righ...

where Ω RN (N 1) is a bounded domain with smooth boundary ∂Ω, ω > 0, m > 1, and b(u) is a nonlinear vector field such that b(u) k u β, with some k > 0, 0 β m 1. f (t) and h(x, t) are ω-periodic (in t) functions. Equation (1.1) is a class of degenerate parabolic equations and appears to be relevant in the theory of non-Newtonian fluids perturbed by nonlinear terms and forced by rather irregular ...

* Correspondence: [email protected] Department of Mathematics, Jiangxi Vocational College of Finance and Economics, Jiujiang, Jiangxi, 332000, PR China Abstract This paper deals with the critical parameter equations for a degenerate parabolic system coupled via nonlinear boundary flux. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence pa...

We consider a finite element approximation of the sixth order nonlinear degenerate parabolic equation ut = ∇.( b(u)∇∆u), where generically b(u) := |u| for any given γ ∈ (0,∞). In addition to showing well-posedness of our approximation, we prove convergence in space dimensions d ≤ 3. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. Finally some num...