Displaying similar documents to “Blow-up Solutions of Quasilinear Hyperbolic Equations With Critical Sobolev Exponent”

Critical Dimensions for counting Lattice Points in Euclidean Annuli

L. Parnovski, N. Sidorova (2010)

Mathematical Modelling of Natural Phenomena

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We study the number of lattice points in ℝ, ≥ 2, lying inside an annulus as a function of the centre of the annulus. The average number of lattice points there equals the volume of the annulus, and we study the and norms of the remainder. We say that a dimension is critical, if these norms do not have upper and lower bounds of the same order as the radius goes to infinity. In [Duke Math. J., 107 (2001),...

Long-Wave Coupled Marangoni - Rayleigh Instability in a Binary Liquid Layer in the Presence of the Soret Effect

A. Podolny, A. A. Nepomnyashchy, A. Oron (2008)

Mathematical Modelling of Natural Phenomena

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We have explored the combined long-wave Marangoni and Rayleigh instability of the quiescent state of a binary- liquid layer heated from below or from above in the presence of the Soret effect. We found that in the case of small Biot numbers there are two long- wave regions of interest ~ and ~ . The dependence of both monotonic and oscillatory thresholds of instability in these regions on both the Soret and dynamic Bond numbers has been investigated....

Wave Equation with Slowly Decaying Potential: asymptotics of Solution and Wave Operators

S. A. Denisov (2010)

Mathematical Modelling of Natural Phenomena

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In this paper, we consider one-dimensional wave equation with real-valued square-summable potential. We establish the long-time asymptotics of solutions by, first, studying the stationary problem and, second, using the spectral representation for the evolution equation. In particular, we prove that part of the wave travels ballistically if ∈ (ℝ) and this result is sharp.