On the Keller-Osserman conjecture in one dimensional case

Osserman Conjecture In

the u.s. policy in central asia and its impact on the colored revolutions in the region (the case study of tulip revolution in kyrgyzstan)

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Four-dimensional Osserman Metrics of Neutral Signature

In the algebraic context, we show that null Osserman, spacelike Osserman, and timelike Osserman are equivalent conditions for a model of signature (2,2). We also classify the null Jordan Osserman models of signature (2,2). In the geometric context, we show that a pseudo-Riemannian manifold of signature (2,2) is null Jordan Osserman if and only if either it has constant sectional curvature or it...

Back to the Keller-Osserman condition for boundary blow-up solutions

This article is concerned with the existence, uniqueness and numerical approximation of boundary blow up solutions for elliptic PDE’s as ∆u = f(u) where f satisfies the so-called Keller-Osserman condition. We characterize existence of such solutions for non-monotone f . As an example, we construct an infinite family of boundary blow up solutions for the equation ∆u = u(1 + cos u) on a ball. We ...

The Stability and Dynamics of a Spike in the One-Dimensional Keller-Segel model

In the limit of a large mass M À 1, and on a finite interval of length 2L, an equilibrium spike solution to the classical Keller-Segel chemotaxis model with a linear chemotactic function is constructed asymptotically. By calculating an asymptotic formula for the translational eigenvalue for M À 1, it is shown that the equilibrium spike solution is unstable to translations of the spike profile. ...