Concept
Helmholtz equation
Related publications (76)
Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs
Fernando José Henriquez Barraza
We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recasting th ...
New York2024Global Regularity For The Nonlinear Wave Equation With Slightly Supercritical Power
Maria Colombo, Silja Noëmi Aline Haffter
We consider the defocusing nonlinear wave equation ❑u D jujp ⠀1u in R3 ⠂ & UOELIG;0; 1/. We prove that for any initial datum with a scaling-subcritical norm bounded by M0 the equation is globally well-posed for p D 5 C i, where i 2 .0; ...
MATHEMATICAL SCIENCE PUBL2023On a Finite-Size Neuronal Population Equation
Tilo Schwalger, Valentin Marc Schmutz, Eva Löcherbach
Population equations for infinitely large networks of spiking neurons have a long tradition in theoret-ical neuroscience. In this work, we analyze a recent generalization of these equations to populations of finite size, which takes the form of a nonlinear ...
SIAM PUBLICATIONS2023Heteroclinic orbits for a system of amplitude equations for orthogonal domain walls
Using a variational method, we prove the existence of heteroclinic solutions for a 6-dimensional system of ordinary differential equations. We derive this system from the classical Benard-Rayleigh problem near the convective instability threshold. The cons ...
ACADEMIC PRESS INC ELSEVIER SCIENCE2023Regularization of multiplicative SDEs through additive noise
We investigate the regularizing effect of certain additive continuous perturbations on SDEs with multiplicative fractional Brownian motion (fBm). Traditionally, a Lipschitz requirement on the drift and diffusion coefficients is imposed to ensure existence ...
2022Acceleration of gossip algorithms through the Euler-Poisson-Darboux Equation
Gossip algorithms and their accelerated versions have been studied exclusively in discrete time on graphs. In this work, we take a different approach and consider the scaling limit of gossip algorithms in both large graphs and large number of iterations. T ...
OXFORD UNIV PRESS2022Subharmonic parametric instability in nearly brimful circular cylinders: a weakly nonlinear analysis
François Gallaire, Alessandro Bongarzone, Francesco Viola
In labscale Faraday experiments, meniscus waves respond harmonically to small-amplitude forcing without threshold, hence potentially cloaking the instability onset of parametric waves. Their suppression can be achieved by imposing a contact line pinned at ...
CAMBRIDGE UNIV PRESS2022Blow-up, partial regularity and turbulence in incompressible fluid dynamics
Weak solutions arise naturally in the study of the Navier-Stokes and Euler equations both from an abstract regularity/blow-up perspective and from physical theories of turbulence. This thesis studies the structure and size of singular set of such weak solu ...
EPFL2022Synthesis of near-diffraction-free orbital-angular-momentum space-time wave packets having a controllable group velocity using a frequency comb
Tobias Kippenberg, Maxim Karpov, Zhe Zhao, Hao Song, Xinzhou Su
Novel forms of light beams carrying orbital angular momentum (OAM) have recently gained interest, especially due to some of their intriguing propagation features. Here, we experimentally demonstrate the generation of near-diffraction-free two-dimensional ( ...
Optica Publishing Group2022Sommerfeld Integrals and Their Relation to the Development of Planar Microwave Devices
This paper deals with the mathematical expressions called Sommerfeld integrals. Introduced by A. Sommerfeld in 1909, they are mathematically equivalent to inverse Hankel transforms. The original historical goal of these integrals was to provide an accurate ...
Piscataway2021