The change in electric potential due to lightning

William W. Hager; Beyza Caliskan Aslan

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 ${(\frac{ℏ}{i} \nabla - A (x))}^{2} u + V (x) u - {f (| u |}^{2}) u = 0 in ℝ^{N} (0.1)$ where $N \geq 3$ , $A : ℝ^{N} \to ℝ^{N}$ is a magnetic potential, possibly unbounded, $V : ℝ^{N} \to ℝ$ 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 $u : ℝ^{N} \to ℂ$ 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...

Unique continuation property near a corner and its fluid-structure controllability consequences

Axel Osses, Jean-Pierre Puel (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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We study a non standard unique continuation property for the biharmonic spectral problem $Δ^{2} w = - λ Δ w$ in a 2D corner with homogeneous Dirichlet boundary conditions and a supplementary third order boundary condition on one side of the corner. We prove that if the corner has an angle $0 < θ_{0} < 2 π$ , $θ_{0} \neq π$ and $θ_{0} \neq 3 π / 2$ , a unique continuation property holds. Approximate controllability of a 2-D linear fluid-structure problem follows from this property, with a control acting on the elastic side of a corner in a domain...