Displaying similar documents to “On the Kuramoto-Sivashinsky equation in a disk”

Nonlinear Heat Equation with a Fractional Laplacian in a Disk

Vladimir Varlamov (1999)

Colloquium Mathematicae

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For the nonlinear heat equation with a fractional Laplacian u t + ( - Δ ) α / 2 u = u 2 , 1 < α ≤ 2, the first initial-boundary value problem in a disk is considered. Small initial conditions, homogeneous boundary conditions, and periodicity conditions in the angular coordinate are imposed. Existence and uniqueness of a global-in-time solution is proved, and the solution is constructed in the form of a series of eigenfunctions of the Laplace operator in the disk. First-order long-time asymptotics of the solution...

An asymptotic approximation of Wallis’ sequence

Vito Lampret (2012)

Open Mathematics

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An asymptotic approximation of Wallis’ sequence W(n) = Πk=1n 4k 2/(4k 2 − 1) obtained on the base of Stirling’s factorial formula is presented. As a consequence, several accurate new estimates of Wallis’ ratios w(n) = Πk=1n(2k−1)/(2k) are given. Also, an asymptotic approximation of π in terms of Wallis’ sequence W(n) is obtained, together with several double inequalities such as, for example, W ( n ) · ( a n + b n ) < π < W ( n ) · ( a n + b n ' ) with a n = 2 + 1 2 n + 1 + 2 3 ( 2 n + 1 ) 2 - 1 3 n ( 2 n + 1 ) ' b n = 2 33 ( n + 1 ) 2 ' b n ' 1 13 n 2 ' n ∈ ℕ .

Poisson sampling for spectral estimation in periodically correlated processes

Vincent Monsan (1994)

Applicationes Mathematicae

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We study estimation problems for periodically correlated, non gaussian processes. We estimate the correlation functions and the spectral densities from continuous-time samples. From a random time sample, we construct three types of estimators for the spectral densities and we prove their consistency.