We propose a second order finite volume scheme for nonlinear degenerate parabolic equations. For some of these models (porous media equation, drift-diffusion system for semiconductors, ...) it has been proved that the transient solution converges to a steady-state when time goes to infinity. The present scheme preserves steady-states and provides a satisfying long-time behavior. Moreover, it re...

In this paper we study the asymptotic behavior of solutions to the damped, nonlinear vibration equation with self-interaction ü = −γu̇+m(‖∇u‖)∆u− δ|u|u+ f, which is known as degenerate if m(·) ≥ 0, and non-degenerate if m(·) ≥ m0 > 0. We would like to point out that, to the author’s knowledge, exponential decay for this type of equations has been studied just for the special cases of α. Our aim ...

In this note we reconsider the continuous time limit of the GARCH(1, 1) process. Let > k and p2 k denote, respectively, the cumulative returns and the volatility processes. We consider the continuous time approximation of the couple (> k , p2 k ). We show that, by choosing di!erent parameterizations, as a function of the discrete interval h, we can obtain either a degenerate or a non-degenerate...

We define the Polish space R of non-degenerate rank-1 systems. Each non-degenerate rank-1 system can be viewed as a measurepreserving transformation of an atomless, σ-finite measure space and as a homeomorphism of a Cantor space. We completely characterize when two non-degenerate rank-1 systems are topologically isomorphic. We also analyze the complexity of the topological isomorphism relation ...

The inputs that satisfy these assumptions may be said to be non-degenerate; otherwise they are degenerate. Implementors are left to their own devices to handle degenerate cases. Some papers may not even list the degenerate inputs. Thus, Forrest [2] deplores the “plethora of special cases ... glossed over by theoretical algorithms”. Forrest, and also Sedgewick [6], calls this the “bugbear” of ge...

Finding the exact, quantum corrected metric on the hypermultiplet moduli space in Type II string compactifications on Calabi-Yau threefolds is an outstanding open problem. We address this issue by relating the quaternionic-Kähler metric on the hypermultiplet moduli space to the complex contact geometry on its twistor space. In this framework, Euclidean D-brane instantons are captured by contact...