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We consider a 1-dimensional Brownian motion whose diffusion coefficient varies when it crosses the origin. We study the long time behavior and we establish different regimes, depending on the variations of the diffusion coefficient:…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
Motivated by the task of computing normalizing constants and importance sampling in high dimensions, we study the dimension dependence of fluctuations for additive functionals of time-inhomogeneous Langevin-type diffusions on…
We establish rigorous quantitative inequalities for the first eigenvalue of the generalized $p$-Robin problem, for both the classical diffusion absorption case, where the Robin boundary parameter $\alpha$ is positive, and the…
Pattern formation mechanisms of a reaction-diffusion-advection system, with one diffusivity, differential advection, and (Robin) boundary conditions of Danckwerts type, are being studied. Pattern selection requires mapping the domains of…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
We investigate the bounds between normal or anomalous effective diffusion for inertial particles transported by parallel flows. The infrared behavior of the fluid kinetic-energy spectrum, i.e. the possible presence of long-range…
This paper explores the classification of parameter spaces for reaction-diffusion systems of two chemical species on stationary domains. The dynamics of the system are explored both in the absence and presence of diffusion. The parameter…
There are many problems that lead to analysis of dynamical systems in which one can distinguish motions of two types: slow one and fast one. An averaging over fast motion is used for approximate description of the slow motion. First…
We consider a semi-infinite spatially dispersive dielectric with unequal transverse and longitudinal susceptibilities. The effect of the boundary is characterized by arbitrary reflection coefficients for polarization waves in the material…
We provide a systematic approach for deducing statistical limit laws via martingale-coboundary decomposition, for nonuniformly hyperbolic systems with slowly contracting and expanding directions. In particular, if the associated return time…
A cross-diffusion system modeling the information herding of individuals is analyzed in a bounded domain with no-flux boundary conditions. The variables are the species' density and an influence function which modifies the information state…
We consider diffusion processes in media with pockets of large diffusivity. The asymptotic behavior of such processes is described when the diffusion coefficients in the pockets tend to infinity. The limiting process is identified as a…
We employ a generalization of Einstein's random walk paradigm for diffusion to derive a class of multidimensional degenerate nonlinear parabolic equations in non-divergence form. Specifically, in these equations, the diffusion coefficient…
In this work an activator-depleted reaction-diffusion system is investigated on polar coordinates with the aim of exploring the relationship and the corresponding influence of domain size on the types of possible diffusion-driven…
This paper, deals with the linear infinite dimensional distributed parameter systems in a Hilbert space where the dynamics of the system is governed by strongly continuous semi-groups. More precisely, for parabolic distributed systems the…
We study the asymptotic behavior of a diffusion process with small diffusion in a domain $D$. This process is reflected at $\partial D$ with respect to a co-normal direction pointing inside $D$. Our asymptotic result is used to study the…
We study diffusions, variational principles and associated boundary value problems on directed graphs with natural weightings. Using random walks and exit times, we associate to certain subgraphs (domains) a pair of sequences, each of which…
This work explores the influence of domain size of a non-compact two dimensional annular domain on the evolution of pattern formation that is modelled by an \textit{activator-depleted} reaction-diffusion system. A closed form expression is…
We observe n possibly dependent random variables, the distribution of which is presumed to be stationary even though this might not be true, and we aim at estimating the stationary distribution. We establish a non-asymptotic deviation bound…