相关论文: Oblique repulsion in the nonnegative quadrant

We study the question of global attraction, in the energy norm, for finite energy solutions to classical particle coupled to a scalar wave field. The attraction could take place to either the set of the stationary solutions in the case of a…

This paper has been withdrawn by the authors. We consider the attraction-repulsion chemotaxis system (3 complicated PDEs system) under homogeneous Neumann boundary conditions in a bounded domain {\Omega} with smooth boundary, then the…

This paper is devoted to the study of the existence and uniqueness of global admissible conservative weak solutions for the periodic single-cycle pulse equation. We first transform the equation into an equivalent semilinear system by…

The existence of random attractors for singular stochastic partial differential equations (SPDE) perturbed by general additive noise is proven. The drift is assumed only to satisfy the standard assumptions of the variational approach to…

We prove the existence of stationary solutions for the density of an infinitely extended plasma interacting with an arbitrary configuration of background charges. Furthermore, we show that the solution cannot be unique if the total charge…

A generic mechanism of collapse in the Gross-Pitaevskii equation with attractive interparticle interactions is gained by reformulating this equation as Newton's equation of motion for a system of particles with a constraint. 'Quantum…

This paper presents a new chaotic system having four attractors, including two fixed point attractors and two symmetrical chaotic strange attractors. Dynamical properties of the system, viz. sensitive dependence on initial conditions,…

Dynamical systems with quadratic or polynomial drift exhibit complex dynamics, yet compared to nonlinear systems in general form, are often easier to analyze, simulate, control, and learn. Results going back over a century have shown that…

The space of polynomial differential equations of a fixed degree with a center singularity has many irreducible components. We prove that pull back differential equations form an irreducible component of such a space. The method used in…

We study a degenerate elliptic system with variable exponents. Using the variational approach and some recent theory on weighted Lebesgue and Sobolev spaces with variable exponents, we prove the existence of at least two distinct nontrivial…

We calculate the non-retarded dispersion force exerted on an electrically polarizable quantum particle by a perfectly conducting toroid, which is one of the most common objects exhibiting a non-trivial topology. We employ a convenient…

We study pullback attractors of non-autonomous non-compact dynamical systems generated by differential equations with non-autonomous deterministic as well as stochastic forcing terms. We first introduce the concepts of pullback attractors…

We consider perimeter perturbations of a class of attractive-repulsive energies, given by the sum of two nonlocal interactions with power-law kernels, defined over sets with fixed measure. We prove that there exists curves in the…

In this note, we consider a Robin-type traction problem for a linearly elastic body occupying an infinite periodically perforated domain. After proving the uniqueness of the solution we use periodic elastic layer potentials to show that the…

We study the existence and long-time asymptotics of weak solutions to a system of two nonlinear drift-diffusion equations that has a gradient flow structure in the Wasserstein distance. The two equations are coupled through a…

Standard textbooks will state that hydrodynamics requires near-equilibrium to be applicable. Recently, however, out-of-equilibrium attractor solutions for hydrodynamics have been found in kinetic theory and holography in systems with a high…

The two ways of constrained systems quantization are considered from the point of view of their self-consistency at the quantum level. With a transparent example of a particle in the external electromagnetic field we demonstrate that the…

Consider an exterior problem of the three-dimensional elastic wave equation, which models the scattering of a time-harmonic plane wave by a rigid obstacle. The scattering problem is reformulated into a boundary value problem by introducing…

In this paper we establish the existence and uniqueness of global solutions (in time), as well as the existence, regularity and stability (upper semicontinuity) of the attractor for the semigroup generated by the solutions of a…

We investigate the in- and out-of-equilibrium phenomena of a rotational impurity -- specifically, a linear molecule -- coupled to a nonconventional environment, a helium nanodroplet. By employing a Lee-Low-Pines-like transformation combined…