Related papers: Well-posedness of Multidimensional Diffusion Proce…
We introduce a new system of surface integral equations for Maxwell's transmission problem in three dimensions. This system has two remarkable features, both of which we prove. First, it is well-posed at all frequencies. Second, the…
We study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for…
We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…
We establish a consistency result by comparing two independent notions of generalised solutions to a large class of linear hyperbolic first order PDE systems with constant coefficients, showing that they eventually coincide. The first is…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
Diffusion models have shown remarkable empirical success in sampling from rich multi-modal distributions. Their inference relies on numerically solving a certain differential equation. This differential equation cannot be solved in closed…
Given a real valued and time-inhomogeneous martingale diffusion X, we investigate the properties of functions defined by the conditional expectation f(t,X_t)=E[g(X_T)|F_t]. We show that whenever g is monotonic or Lipschitz continuous then…
Diffusion models have demonstrated exceptional performances in various fields of generative modeling, but suffer from slow sampling speed due to their iterative nature. While this issue is being addressed in continuous domains, discrete…
We construct non-negative martingale solutions to the stochastic porous medium equation in one dimension with homogeneous Dirichlet boundary conditions which exhibit a type of sticky behavior at zero. The construction uses the stochastic…
For a class of stochastic differential equations with reflection for which a certain ${\mathbb{L}}^p$ continuity condition holds with $p>1$, it is shown that any weak solution that is a strong Markov process can be decomposed into the sum…
This paper develops solutions of fractional Fokker-Planck equations describing subdiffusion of probability densities of stochastic dynamical systems driven by non-Gaussian L\'evy processes, with space-time-dependent drift, diffusion and…
We consider a system of partial differential equations describing mass transport in a multicomponent isothermal compressible fluid. The diffusion fluxes obey the Fick-Onsager or Maxwell-Stefan closure approach. Mechanical forces result into…
A variety of enhanced statistical and numerical methods are now routinely used to extract comprehensible and relevant thermodynamic information from the vast amount of complex, high-dimensional data obtained from intensive molecular…
In this paper, we obtain the low order global well-posedness and the asymptotic behavior of solution of 2D MHD problem with partial dissipation in half space with non-slip boundary condition. When magnetic field equal zero, the system be…
We provide a set of conditions that is necessary and sufficient for the $L^{2}$-wellposedness of the Cauchy problem for fifth and sixth order variable-coefficient linear dispersive equations. The necessity of these conditions had been…
It is well-known that one-dimensional time fractional diffusion-wave equations with variable coefficients can be reduced to ordinary fractional differential equations and systems of linear fractional differential equations via scaling…
This paper presents analogous results for stochastic fast-diffusion equations. Since the fast-diffusion equation possesses weaker dissipativity than the porous medium one does, some technical difficulties appear in the study. As a…
This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time-changed by an inverse stable subordinator whose index equals the order of…
To characterize the Neumann problem for nonlinear Fokker-Planck equations, we investigate distribution dependent reflecting SDEs (DDRSDEs) in a domain. We first prove the well-posedness and establish functional inequalities for reflecting…
The paper is devoted to well-posedness analysis and the numerical solution of a family of general elliptic mixed variational-hemivariational inequalities. Various mixed variational equations, mixed variational inequalities and mixed…