Displaying similar documents to “The change in electric potential due to lightning”

Multi-peak solutions for magnetic NLS equations without non-degeneracy conditions

Silvia Cingolani, Louis Jeanjean, Simone Secchi (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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In this work we consider the magnetic NLS equation ( ℏ i ∇ - A ( x ) ) 2 u + V ( x ) u - f ( | u | 2 ) u = 0 in ℝ N ( 0 . 1 ) where N ≥ 3 , A : ℝ N → ℝ N is a magnetic potential, possibly unbounded, V : ℝ N → ℝ is a multi-well electric potential, which can vanish somewhere, is a subcritical nonlinear term. We prove the existence of a semiclassical multi-peak solution u : ℝ N → ℂ to (0.1), under conditions on the nonlinearity which are nearly optimal.

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

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We study the linearized water-wave problem in a bounded domain ( a finite pond of water) of ℝ 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...