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Radially symmetric solutions of the Poisson-Boltzmann equation with a given energy

Tadeusz Nadzieja, Andrzej Raczyński (2000)

Applicationes Mathematicae

We consider the following problem: Δ Φ = ± M ο v e r Ω e - Φ / Θ e - Φ / Θ , E = M Θ 1 ο v e r 2 Ω | Φ | 2 , Φ | Ω = 0 , where Φ: Ω ⊂ n → ℝ is an unknown function, Θ is an unknown constant and M, E are given parameters.

Radiation conditions at the top of a rotational cusp in the theory of water-waves

Sergey A. Nazarov, Jari Taskinen (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We study the linearized water-wave problem in a bounded domain (e.g.a finite pond of water) of 3 , having a cuspidal boundary irregularity created by a submerged body. In earlier publications the authors discovered that in this situation the spectrum of the problem may contain a continuous component in spite of the boundedness of the domain. Here, we proceed to impose and study radiation conditions at a point 𝒪 of the water surface, where a submerged body touches the surface (see Fig. 1). The radiation...

Radiation conditions at the top of a rotational cusp in the theory of water-waves

Sergey A. Nazarov, Jari Taskinen (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

We study the linearized water-wave problem in a bounded domain (e.g. a finite pond of water) of 3 , having a cuspidal boundary irregularity created by a submerged body. In earlier publications the authors discovered that in this situation the spectrum of the problem may contain a continuous component in spite of the boundedness of the domain. Here, we proceed to impose and study radiation conditions at a point 𝒪 of the water surface, where a submerged body touches the surface (see Fig. 1)....

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