相关论文: Localization in stationary non-equilibrium solutio…

We present a general formalism able to derive the kinetic equations of polymer dynamics. It is based on the application of nonequilibrium thermodynamics to analyze the irreversible processes taking place in the conformational space of the…

We study convergence in variation of probability solutions of nonlinear Fokker-Planck-Kolmogorov equations to stationary solutions. We obtain sufficient conditions for the exponential convergence of solutions to the stationary solution in…

The main goal of this paper is to study the nature of the support of the solution of suitable nonlinear Schr\"{o}dinger equations mainly the compactness of the support and its spatial localization. This question is very related with pure…

A stochastic Schr\"odinger equation is presented to describe simultaneous continuous measurement of the position and momentum of a non-relativistic particle. The equation is solved to yield a state localised in position and momentum…

We consider Smoluchowski's coagulation equation with a kernel of the form $K = 2 + \epsilon W$, where $W$ is a bounded kernel of homogeneity zero. For small $\epsilon$, we prove that solutions approach a universal, unique self-similar…

We present a new approach for search of coexisting classes of localised modes admitted by the repulsive (defocusing) scalar or vector nonlinear Schr\"odinger-type equations. The approach is based on the observation that generic solutions of…

We revisit the classic stability problem of the buckling of an inextensible, axially compressed beam on a nonlinear elastic foundation with a semi-analytical approach to understand how spatially localized deformation solutions emerge in…

In this paper we prove the existence of a family of self-similar solutions for a class of coagulation equations with a constant flux of particles from the origin. These solutions are expected to describe the longtime asymptotics of…

The Smoluchowski equation is a system of partial differential equations modelling the diffusion and binary coagulation of a large collection of tiny particles. The mass parameter may be indexed either by positive integers, or by positive…

Generic inhomogeneous steady states in an asymmetric exclusion process on a ring with a pair of point bottlenecks are studied. We show that, due to an underlying universal feature, measurements of coarse-grained steady-state densities in…

Sufficient conditions are given for existence and uniqueness in Smoluchowski's coagulation equation, for a wide class of coagulation kernels and initial mass distributions. An example of non-uniqueness is constructed. The stochastic…

In this paper we study the fundamental solution of the equation obtained by the linearisation of the Smoluchowski coagulation equation with the multiplicative kernel $(x y)^{\lambda/2}$ with $\lambda\in (1, 2)$ around the steady state…

The paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete, and the binary aggregation alone governs the time evolution of the systems. By considering the growth…

We provide new results regarding the localization of the solutions of nonlinear operator systems. We make use of a combination of Krasnosel'ski\u{\i} cone compression-expansion type methodologies and Schauder-type ones. In particular we…

In this article we prove the existence of solutions to the singular coagulation equation with multifragmentation. We use weighted $L^1$-spaces to deal with the singularities and to obtain regular solutions. The Smoluchowski kernel is…

We propose an explicit construction of a stationary solution for a stochastic recursion of the form $X\circ\theta=\phi(X)$ on a partially-ordered Polish space, when the monotonicity of $\phi$ is not assumed. Under certain conditions, we…

We prove global well-posedness and scattering for solutions to the mass-critical inhomogeneous nonlinear Schr\"odinger equation $i\partial_{t}u+\Delta u=\pm |x|^{-b}|u|^{\frac{4-2b}{d}}u$ for large $L^2(\mathbb{R} ^d)$ initial data with…

We prove that a system of locally interacting diffusions carrying discrete masses, subject to an environmental noise and undergoing mass coagulation, converges to a system of Stochastic Partial Differential Equations (SPDEs) with…

We develop a framework for localized source detection in dynamical systems governed by nonlinear partial differential equations based on first and second-order sensitivity analysis. Building on the standard adjoint formulation, which…

We consider the Hamiltonian system of scalar wave field and a single nonrelativistic particle coupled in a translation invariant manner. The particle is also subject to a confining external potential. The stationary solutions of the system…