Two-dimensional Keller-Segel model: Optimal critical mass and qualitative properties of the solutions.

Blanchet, Adrien; Dolbeault, Jean; Perthame, Benoit

Displaying similar documents to “Two-dimensional Keller-Segel model: Optimal critical mass and qualitative properties of the solutions.”

Oscillation of Mertens’ product formula

Harold G. Diamond, Janos Pintz (2009)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Mertens’ product formula asserts that $\prod_{p \leq x} (1 - \frac{1}{p}) log x \to e^{- γ}$ as $x \to \infty$ . Calculation shows that the right side of the formula exceeds the left side for $2 \leq x \leq 10^{8}$ . It was suggested by Rosser and Schoenfeld that, by analogy with Littlewood’s result on $π (x) - li x$ , this and a complementary inequality might change their sense for sufficiently large values of $x$ . We show this to be the case.

Second-order boundary estimates for solutions to singular elliptic equations in borderline cases.

Anedda, Claudia, Porru, Giovanni (2011)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Similarity:

Perfect powers in the summatory function of the power tower

Florian Luca, Diego Marques (2010)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let ${(a_{n})}_{n \geq 1}$ be the sequence given by $a_{1} = 1$ and $a_{n} = n^{a_{n - 1}}$ for $n \geq 2$ . In this paper, we show that the only solution of the equation $a_{1} + \dots + a_{n} = m^{l}$ is in positive integers $l > 1, m$ and $n$ is $m = n = 1$ .

Another relation between π, e, γ and ζ(n).

Luis J. Boya (2008)

RACSAM

Similarity:

Enumeration of binary trees and universal types.

Knessl, Charles, Szpankowski, Wojciech (2005)

Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]

Similarity:

A note on directed polymers in Gaussian environments.

Hu, Yueyun, Shao, Qi-Man (2009)

Electronic Communications in Probability [electronic only]

Similarity:

Explicit lower bounds for linear forms in two logarithms

Nicolas Gouillon (2006)

Journal de Théorie des Nombres de Bordeaux

Similarity:

We give an explicit lower bound for linear forms in two logarithms. For this we specialize the so-called Schneider method with multiplicity described in []. We substantially improve the numerical constants involved in existing statements for linear forms in two logarithms, obtained from Baker’s method or Schneider’s method with multiplicity. Our constant is around $5 . 10^{4}$ instead of $10^{8}$ .

On the Poisson approximation of the binomial distribution.

Ruzankin, P.S. (2001)

Sibirskij Matematicheskij Zhurnal

Similarity:

Mean value of Piltz' function over integers free of large prime factors.

Nyandwi, Servat (2003)

Publications de l'Institut Mathématique. Nouvelle Série

Similarity: