Abstract. A nonlinear fourth-order parabolic equation with nonhomogeneous Dirichlet–Neumann boundary conditions in one space dimension is analyzed. This equation appears, for instance, in quantum semiconductor modeling. The existence and uniqueness of strictly positive classical solutions to the stationary problem are shown. Furthermore, the existence of global nonnegative weak solutions to the...

We investigate the long time behavior of the critical mass Patlak-Keller-Segel equation. This equation has a one parameter family of steady-state solutions ̺λ, λ > 0, with thick tails whose second moment is not bounded. We show that these steady state solutions are stable, and find basins of attraction for them using an entropy functional Hλ coming from the critical fast diffusion equation in R ...

Mobile ad-hoc networks (MANETs) are dynamic by nature; this dynamism comes from node mobility, traffic congestion, and other transmission conditions. Metrics to evaluate the effects of those conditions shine a light on node's behavior in an ad-hoc network, helping to identify the node or nodes with better conditions of connection. In this paper, we propose a relative index to evaluate a single ...

Image retrieval is the important technique in image processing. The paper presents the robust object recognition using texture and directional feature extraction. The system proposes texture descriptors such as fast discrete Curvelet transform based entropy feature and local directional pattern. The category recognition is to classify an object into one of several predefined categories. The Fas...

The global existence of non-negative weak solutions to a strongly coupled parabolic system arising in population dynamics is shown. The cross-diffusion terms are allowed to be arbitrarily large, whereas the self-diffusion terms are assumed to vanish. The last assumption complicates the analysis since these terms usually provide H estimates of the solutions. The existence proof is based on a pos...

In this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. It is shown that it generates the Kolmogorov entropy as a special case. If $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.

The physical concept of entropy as it is used in thermodynamics is related to the mathematical formulation of a Shannon entropy. Usually only the Shannon entropy of equilibrium distributions such as a canonical distribution is considered. Large deviations statistics goes beyond that framework. Entropies are considered for arbitrary distributions or physical states, and they describe, e.g., \how...

Abstract. In this paper, we prove new functional inequalities of Poincaré type on the one-dimensional torus S and explore their implications for the long-time asymptotics of periodic solutions of nonlinear singular or degenerate parabolic equations of second and fourth order. We generically prove a global algebraic decay of an entropy functional, faster than exponential for short times, and an ...