Related papers: Optimal stopping of one-dimensional diffusions wit…
We use a deterministic particle method to produce numerical approximations to the solutions of an evolution cross-diffusion problem for two populations. According to the values of the diffusion parameters related to the intra and…
In this manuscript we consider a class optimal control problem for stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we…
We derive continuous dependence estimates for weak entropy solutions of degenerate parabolic equations with nonlinear fractional diffusion. The diffusion term involves the fractional Laplace operator, $\Delta^{\alpha/2}$ for $\alpha \in…
In this paper, we discuss initial-boundary value problems for linear diffusion equation with multiple time-fractional derivatives. By means of the Mittag-Leffler function and the eigenfunction expansion, we reduce the problem to an integral…
We study the optimal stopping problem of McKean-Vlasov diffusions when the criterion is a function of the law of the stopped process. A remarkable new feature in this setting is that the stopping time also impacts the dynamics of the…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
This paper studies a central planner's decision making on behalf of a group of members with diverse discount rates. In the context of optimal stopping, we work with an aggregation preference to incorporate all discount rates via an attitude…
The equation which describes a particle diffusing in a logarithmic potential arises in diverse physical problems such as momentum diffusion of atoms in optical traps, condensation processes, and denaturation of DNA molecules. A detailed…
In this paper, we develop a modified nonlinear dynamic diffusion (DD) finite element method for convection-diffusion-reaction equations. This method is free of stabilization parameters and is capable of precluding spurious oscillations. We…
We consider a class of exit time stochastic control problems for diffusion processes with discounted criterion, where the controller can utilize a given amount of resource, called "fuel". In contrast to the vast majority of existing…
Splitting methods constitute a well-established class of numerical schemes for solving convection-diffusion-reaction problems. They have been shown to be effective in solving problems with periodic boundary conditions. However, in the case…
An implicit Euler finite-volume scheme for general cross-diffusion systems with volume-filling constraints is proposed and analyzed. The diffusion matrix may be nonsymmetric and not positive semidefinite, but the diffusion system is assumed…
In this article we consider the ergodic risk-sensitive control problem for a large class of multidimensional controlled diffusions on the whole space. We study the minimization and maximization problems under either a blanket stability…
This work presents a comprehensive framework for enhanced diffusion modeling in fluid-structure interactions by combining the Immersed Boundary Method (IBM) with stochastic trajectories and high-order spectral boundary conditions. Using…
We consider the problem of identifying a sparse initial source condition to achieve a given state distribution of a diffusion-advection partial differential equation after a given final time. The initial condition is assumed to be a finite…
The paper is a full version of the short presentation in \cite{amv17}. Ergodic control for one-dimensional controlled diffusion is tackled; both drift and diffusion coefficients may depend on a strategy which is assumed markovian. Ergodic…
In this paper we consider a one-dimensional diffusion equation on the interval $[0,1]$ satisfying non-Feller boundary conditions. As a consequence, the initial value Cauchy problem fails to preserve nonnegativity or boundedness.…
In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by introducing a generalized backward stochastic differential…
Consider the initial-boundary value problem for the 2-speed Carleman model of the Boltzmann equation of the kinetic theory of gases set in some bounded interval with boundary conditions prescribing the density of particles entering the…
Nonnegative directional splittings of anisotropic diffusion operators in the divergence form are investigated. Conditions are established for nonnegative directional splittings to hold in a neighborhood of an arbitrary interior point. The…