相关论文: Stationary Directed Polymers and Energy Solutions …

In this paper we study second order stochastic differential equations with measurable and density-distribution dependent coefficients. Through establishing a maximum principle for kinetic Fokker-Planck-Kolmogorov equations with…

We are concerned with the radially symmetric stationary wave for the exterior problem of two-dimensional Burgers equation. A sufficient and necessary condition to guarantee the existence of such a stationary wave is given and it is also…

Systems consisting of a single ordinary differential equation coupled with one reaction-diffusion equation in a bounded domain and with the Neumann boundary conditions are studied in the case of particular nonlinearities from the…

We examine the merits of using a family of polynomials that are orthogonal with respect to a non-classical weight function to discretize the speed variable in continuum kinetic calculations. We consider a model one-dimensional partial…

A generalization of the Hopf-Cole transformation and its relation to the Burgers equation of integer order and the diffusion equation with quadratic nonlinearity are discussed. The explicit form of a particular analytical solution is…

In this work, we prove the strong Feller property and the exponential ergodicity of stochastic Burgers equations driven by $\alpha/2$-subordinated cylindrical Brownian motions with $\alpha\in(1,2)$. To prove the results, we truncate the…

Statistical invariance of Wiener increments under SO(n) rotations provides a notion of gauge transformation of state-dependent Brownian motion. We show that the stochastic dynamics of non gauge-invariant systems is not unambiguously…

The spectral theory for weakly stationary processes valued in a separable Hilbert space has known renewed interest in the past decade. Here we follow earlier approaches which fully exploit the normal Hilbert module property of the time…

We introduce and analyze a broad class of continuous directed polymers in $\mathbb{R}^d$ driven by Gaussian environments that are white in time and spatially correlated, under Dalang's condition. Using an It\^o-renormalized…

The self-repelling Brownian polymer model (SRBP) initiated by Durrett and Rogers in [Durrett-Rogers (1992)] is the continuous space-time counterpart of the myopic (or 'true') self-avoiding walk model (MSAW) introduced in the physics…

This paper represents a mixed numerical method for the multi-resolution solution of non-linear partial differential equations based on B-Spline wavelets. The method is based on a second-order finite difference formula combined with the…

The phenomenon of steady streaming, or acoustic streaming, is an important physical phenomenon studied extensively in the literature. Its mathematical formulation involves the Navier-Stokes equations, thus due to the complexity of these…

Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of asymptotic stability of bounded, discontinuous or…

We solve the time-dependent Fokker-Planck equation for a two-dimensional active Brownian particle exploring a circular region with an absorbing boundary. Using the passive Brownian particle as basis states and dealing with the activity as a…

A new mean-field type theory is proposed to study order-disorder transitions (ODT) in block copolymers. The theory applies to both the weak segregation (WS) and the strong segregation (SS) regimes. A new energy functional is proposed…

We propose new type of $q$-diffusive heat equation with nonsymmetric $q$-extension of the diffusion term. Written in relative gradient variables this system appears as the $q$- viscous Burgers' equation. Exact solutions of this equation in…

We construct space-time stationary solutions of the 1D Burgers equation with random forcing in the absence of periodicity or any other compactness assumptions. More precisely, for the forcing given by a homogeneous Poissonian point field in…

We analyze the diffusion of a Brownian particle in a fluid under stationary flow. By using the scheme of non-equilibrium thermodynamics in phase space, we obtain the Fokker-Planck equation which is compared with others derived from kinetic…

For a Brownian directed polymer in a Gaussian random environment, with $q(t,\cdot)$ denoting the quenched endpoint density and \[ Q_n(t,x_1,\ldots,x_n)=\mathbf{E}[q(t,x_1)\ldots q(t,x_n)], \] we derive a hierarchical PDE system satisfied by…

We study a finite-element based space-time discretisation for the 2D stochastic Navier-Stokes equations in a bounded domain supplemented with no-slip boundary conditions. We prove optimal convergence rates in the energy norm with respect to…