Related papers: Weak universality for a class of 3d stochastic rea…
The fast reaction limit for a nonlinear bulk-surface reaction-diffusion system is investigated. This system describes a reversible reaction with arbitrary stoichiometric coefficients, where one chemical is present in a bounded vessel…
We study a quasilinear parabolic Cauchy problem with a cumulative distribution function on the real line as an initial condition. We call 'probabilistic solution' a weak solution which remains a cumulative distribution function at all…
The scaling form of the whole distribution P(D) of the random diffusion coefficient D(x) in a model of classically diffusing particles is investigated. The renormalization group approach above the lower critical dimension d=0 is applied to…
We consider a $4\times4$ nonlinear reaction-diffusion system posed on a smooth domain $\Omega$ of $\mathbb{R}^N$ ($N \geq 1$) with controls localized in some arbitrary nonempty open subset $\omega$ of the domain $\Omega$. This system is a…
We study the existence of weak solutions to a Cahn--Hilliard--Darcy system coupled with a convection-reaction-diffusion equation through the fluxes, through the source terms and in Darcy's law. The system of equations arises from a mixture…
In this paper, we study the null and approximate controllability of a class of fully nonlocal coupled stochastic reaction--convection--diffusion systems. The system consists of two forward stochastic parabolic equations driven by general…
This note shows how classical tools from linear control theory can be leveraged to provide a global analysis of nonlinear reaction-diffusion models. The approach is differential in nature. It proceeds from classical tools of contraction…
We consider fully nonlinear Hamilton-Jacobi-Bellman equations associated to diffusion control problems involving a finite set-valued (or switching) control and possibly a continuum-valued control. We construct a lower complexity…
Copulas, generalized estimating equations, and generalized linear mixed models promote the analysis of grouped data where non-normal responses are correlated. Unfortunately, parameter estimation remains challenging in these three…
We analyze energy spreading for a system that features mixed chaotic phase-space, whose control parameters (or slow degrees of freedom) vary quasi-statically. For demonstration purpose we consider the restricted 3~body problem, where the…
In this paper we prove a weak necessary and sufficient maximum principle for Markovian regime switching stochastic optimal control problems. Instead of insisting on the maximum condition of the Hamiltonian, we show that 0 belongs to the sum…
Diffusion preserves the positivity of concentrations, therefore, multicomponent diffusion should be nonlinear if there exist non-diagonal terms. The vast variety of nonlinear multicomponent diffusion equations should be ordered and special…
We give a probabilistic interpretation of the Monte Carlo scheme proposed by Fahim, Touzi and Warin [Ann. Appl. Probab. 21 (2011) 1322-1364] for fully nonlinear parabolic PDEs, and hence generalize it to the path-dependent (or…
Recently, we proposed a method to estimate parameters of stochastic dynamics based on the linear response statistics. The method rests upon a nonlinear least-squares problem that takes into account the response properties that stem from the…
We consider a mathematical model for heterogeneous catalysis in a finite three-dimensional pore of cylinder-like geometry, with the lateral walls acting as a catalytic surface. The system under consideration consists of a…
Weakly chaotic or weakly interacting systems have a wide regime where the common random matrix theory modeling does not apply. As an example we consider cold atoms in a nearly integrable optical billiard with displaceable wall ("piston").…
Consider $F$ an element of the second Wiener chaos with variance one. In full generality, we show that, for every integer $p\ge 1$, there exists $\eta_p>0$ such that if $\kappa_4(F)<\eta_p$ then the Malliavin derivative of $F$ admits a…
The transport of excitation probabilities amongst weakly coupled subunits is investigated for a class of finite quantum systems. It is demonstrated that the dynamical behavior of the transported quantity depends on the considered length…
We consider a nonlinear reaction--diffusion equation in a domain consisting of two bulk regions connected via small channels periodically distributed within a thin layer. The height and the thickness of the channels are of order $\epsilon$,…
In the present work, we investigate stochastic third grade fluids equations in a $d$-dimensional setting, for $d = 2, 3$. More precisely, on a bounded and simply connected domain $\mathcal{D}$ of $\mathbb{R}^d$, $d = 2,3$, with a…