Erratum: “On a fourth order degenerate parabolic equation in higher space dimension” [J. Math. Phys. 50, 123524 (2009)]

On a Fourth Order Degenerate Parabolic Equation: Global Entropy Estimates, Existence and Qualitative Behaviour of Solutions

By means of energy and entropy estimates, we prove existence and positivity results in higher space dimensions for degenerate parabolic equations of fourth order with nonnegative initial values. We discuss their asymptotic behaviour for t ! 1 and give a counterexample to uniqueness. 0. Introduction In this paper we will present new results on existence, (non)uniqueness, positivity and asymptoti...

On a Fourth-order Degenerate Parabolic Equation: Global Entropy Estimates, Existence, and Qualitative Behavior of Solutions

By means of energy and entropy estimates, we prove existence and positivity results in higher space dimensions for degenerate parabolic equations of fourth order with nonnegative initial values. We discuss their asymptotic behavior for t → ∞ and give a counterexample to uniqueness.

Finite element approximation of a fourth order nonlinear degenerate parabolic equation

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...

Solutions of a Fourth Order Degenerate Parabolic Equation with Weak Initial Trace

We show that the nonlinear fourth order degenerate parabolic equation u t + div (u n ru) = 0; n > 0 admits nonnegative solutions to initial data which are a nonnegative Radon measure provided that n < 2. In addition, we prove that the equation has a regularizing eeect in the sense that the solution we construct is in H 1 (R N) for all positive times and in H 2 loc (R N) for almost all positive ...

Blow-Up in a Fourth-Order Semilinear Parabolic Equation From . . .