Related papers: Local amplitude equation from non-local dynamics
In this work we investigate a boundary problem with non-local conditions for mixed parabolic-hyperbolic type equation with three lines of type-changing with Caputo fractional derivative in the parabolic part. We equivalently reduce…
We prove the wellposedness of scalar wave equations on spatially flat universe as a background with nonminimal coupling with the scalar potential turned on by introducing the $k$-order linear energy and the corresponding energy norm. In the…
Within the framework of Hilbert spaces, we solve nonlocal problems in bounded domains with prescribed conditions on the complement of the domain. Our main focus is on the inhomogeneous Neumann problem in a rather general setting. We also…
The normal field instability in magnetic liquids is investigated experimentally by means of a radioscopic technique which allows a precise measurement of the surface topography. The dependence of the topography on the magnetic field is…
We consider the 3D compressible isentropic Euler equations describing the motion of a liquid in an unbounded initial domain with a moving boundary and a fixed flat bottom at finite depth. The liquid is under the influence of gravity and…
We study wave turbulence in systems with two special properties: a large number of fields (large $N$) and a nonlinear interaction that is strongly local in momentum space. The first property allows us to find the kinetic equation at all…
This paper investigates the local boundedness of weak solutions to a direction-dependent double-phase nonlocal elliptic equation. By employing refined energy estimates and De Giorgi-type techniques, we establish the local boundedness of…
The Hubbard model on a semi-infinite three-dimensional lattice is considered to investigate electron-correlation effects at single-crystal surfaces. The standard second-order perturbation theory in the interaction U is used to calculate the…
We investigate the physical-space locality of interactions in three-dimensional incompressible turbulent flow. To that, we modify the nonlinear terms of the vorticity equation such that the vorticity field is advected and stretched by the…
We study equations from the area of peridynamics, which is an extension of elasticity. The governing equations form a system of nonlocal wave equations. Its governing operator is found to be a bounded, linear and self-adjoint operator on a…
We consider an inverse problem for a Westervelt type nonlinear wave equation with fractional damping. This equation arises in nonlinear acoustic imaging, and we show the forward problem is locally well-posed. We prove that the smooth…
The paper deals with three evolution problems arising in the physical modelling of acoustic phenomena of small amplitude in a fluid, bounded by a surface of extended reaction. The first one is the widely studied wave equation with acoustic…
The nonlinear dynamics of the free surface of an ideal conducting liquid in a strong external electric field is studied. It is establish that the equations of motion for such a liquid can be solved in the approximation in which the surface…
We study a new type of large-scale instability, which arises in obliquely rotating stratified electroconductive fluid with an external uniform magnetic field and a small-scale external force having zero helicity. This force gives rise to…
We prove the local well-posedness of the 3D free-boundary incompressible elastodynamics with surface tension describing the motion of an elastic medium in a periodic domain with a moving graphical surface. The deformation tensor is assumed…
For a system of equations describing one-dimensional nonlinear oscillations in a magnetoactive plasma, we study the effect of a constant magnetic field on the breaking of oscillations. For the nonrelativistic case, a criterion for the…
We study the well-posedness of a class of nonlocal-interaction equations on general domains $\Omega\subset \mathbb{R}^d$, including nonconvex ones. We show that under mild assumptions on the regularity of domains (uniform prox-regularity),…
The conceptual basis for the nonlocality of accelerated systems is presented. The nonlocal theory of accelerated observers and its consequences are briefly described. Nonlocal field equations are developed for the case of the…
We consider a class of finite-dimensional dynamical systems whose equations of motion are derived from a non-local-in-time action principle. The action functional has a zeroth order piece derived from a local Hamiltonian and a perturbation…
The MMT equation was proposed by Majda, McLaughlin and Tabak as a model to study wave turbulence. We focus on the kinetic equation associated to this Hamiltonian system, which is believed to give a way to predict turbulent spectra. We…