Related papers: Hamilton-Jacobi method for molecular distribution …
We explain the ubiquity and extremely slow evolution of non gaussian out-of-equilibrium distributions for the Hamiltonian Mean-Field model, by means of traditional kinetic theory. Deriving the Fokker-Planck equation for a test particle, one…
We use the adjoint methods to study the static Hamilton-Jacobi equations and to prove the speed of convergence for those equations. The main new ideas are to introduce adjoint equations corresponding to the formal linearizations of…
We develop an efficient method to calculate probabilities of large deviations from the typical behavior (rare events) in reaction--diffusion systems. The method is based on a semiclassical treatment of underlying "quantum" Hamiltonian,…
For the particles undergoing the anomalous diffusion with different waiting time distributions for different internal states, we derive the Fokker-Planck and Feymann-Kac equations, respectively, describing positions of the particles and…
We consider an extension of the well-known Hamilton-Jacobi-Bellman (HJB) equation for fractional order dynamical systems in which a generalized performance index is considered for the related optimal control problem. Owing to the…
We study the large time behavior of the sublinear viscosity solution to a singular Hamilton-Jacobi equation that appears in a critical Coagulation-Fragmentation model with multiplicative coagulation and constant fragmentation kernels. Our…
We prove explicit estimates for the error in random homogenization of degenerate, second-order Hamilton-Jacobi equations, assuming the coefficients satisfy a finite range of dependence. In particular, we obtain an algebraic rate of…
In our previous papers [11,13] we showed that the Hamilton-Jacobi problem can be regarded as a way to describe a given dynamics on a phase space manifold in terms of a family of dynamics on a lower-dimensional manifold. We also showed how…
The Hamilton-Jacobi equation on metric spaces has been studied by several authors; following the approach of Gangbo and Swiech, we show that the final value problem for the Hamilton-Jacobi equation has a unique solution even if we add a…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
We explore the approximation of feedback control of integro-differential equations containing a fractional Laplacian term. To obtain feedback control for the state variable of this nonlocal equation we use the Hamilton--Jacobi--Bellman…
We investigate in this work a fully-discrete semi-Lagrangian approximation of second order possibly degenerate Hamilton-Jacobi-Bellman (HJB) equations on a bounded domain with oblique boundary conditions. These equations appear naturally in…
Combing the weak KAM method for contact Hamiltonian systems and the theory of viscosity solutions for Hamilton-Jacobi equations, we study the Lyapunov stability and instability of viscosity solutions for evolutionary contact Hamilton-Jacobi…
The homotopy analysis method known from its successful applications to obtain quasi-analytical approximations of solutions of ordinary and partial differential equations is applied to stochastic differential equations with Gaussian…
We develop a general framework for response theory in diffusion processes governed by Fokker-Planck equations, based on the notion of the Dissipation Function. Using the analytically solvable Brownian oscillator model, we derive exact…
We study the asymptotic behavior of solutions to the Dirichlet problem for Hamilton-Jacobi equations with large drift terms, where the drift terms are given by the Hamiltonian vector fields of Hamiltonian $H$. This is an attempt to…
For non convex Hamiltonians, the viscosity solution and the more geometric minimax solution of the Hamilton-Jacobi equation do not coincide in general. They are nevertheless related: we show that iterating the minimax procedure during…
Recently the Hamilton-Jacobi formulation for first order constrained systems has been developed. In such formalism the equations of motion are written as total differential equations in many variables. We generalize the Hamilton-Jacobi…
We investigate the multi-chain version of the Chemical Master Equation, when there are transitions between different states inside the long chains, as well as transitions between (a few) different chains. In the discrete version, such a…
This paper develops a comprehensive Hamilton-Jacobi framework to analyze asymptotic propagation dynamics in a field-road system featuring unidirectional advection and Wentzell-type boundary conditions. We rigorously derive a Hamilton-Jacobi…