Related papers: A conservative stochastic Dirac-Klein-Gordon syste…
We present a new a-priori estimate for discrete coagulation-fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this…
We analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the…
We consider a stochastic partial differential equation with two logarithmic nonlinearities, with two reflections at 1 and -1 and with a constraint of conservation of the space average. The equation, driven by the derivative in space of a…
We consider the Cauchy problem of coupled 3-D wave and Klein-Gordon equations with a quadratic form of nonlinearity. We show global existence under several conditions, including large derivative data for wave equations and the null…
We consider an ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, which we call the relativistic Vlasov-Klein-Gordon system, we prove the existence of…
We prove that the Cauchy problem for the Dirac-Klein-Gordon system of equations in 1D is globally well-posed in a range of Sobolev spaces of negative index for the Dirac spinor and positive index for the scalar field. The main ingredient in…
We show that the Cauchy Problem for a randomly forced, periodic multi-dimensional scalar first-order conservation law with additive or multiplicative noise is well-posed: it admits a unique solution, characterized by a kinetic formulation…
We establish the large deviation principle for the slow variables in slow-fast dynamical system driven by both Brownian noises and L\'evy noises. The fast variables evolve at much faster time scale than the slow variables, but they are…
We consider a class of nonlinear Klein-Gordon equations which are Hamiltonian and are perturbations of linear dispersive equations. The unperturbed dynamical system has a bound state, a spatially localized and time periodic solution. We…
In the present paper, we study the semi-classical approximation of a Yukawa-coupled massive Dirac-Klein-Gordon system with some general nonlinear self-coupling. We prove that for a constrained coupling constant there exists a family of…
In this paper, we consider the well-posedness of stochastic S-KdV driven by multiplicative noises in $H_x^1\times H_x^1$. To get the local well-posedness, we first develop the bilinear and trilinear Bourgain norm estimates of the nonlinear…
We consider the generalized almost periodic homogenization problem for two different types of stochastic conservation laws with oscillatory coefficients and multiplicative noise. In both cases the stochastic perturbations are such that the…
This paper discusses the initial-boundary value problem (with a nonhomogeneous boundary condition) for a multi-dimensional scalar first-order conservation law with a multiplicative noise. One introduces a notion of kinetic formulations in…
The computational analysis of the Cauchy problem for semi-linear Klein-Gordon equations in the de Sitter spacetime is considered. Several simulations are performed to show the time-global behaviors of the solutions of the equations in the…
We study the Cauchy problems for the Hartree-type nonlinear Dirac equations with Yukawa-type potential in two and three spatial dimensions. This paper improves our previous results \cite{chohlee,cholee}; we establish global well-posedness…
The Cauchy problem for the classical Dirac-Klein-Gordon system in two space dimensions is globally well-posed for L^2 Schoedinger data and wave data in H^{1/2} \times H^{-1/2}. In the case of smooth data there exists a global smooth…
This paper focuses on the long-term behavior of solutions to nonlinear stochastic Fokker-Planck equations driven by common noise, where the drift term has a linear dependence on the measure. These equations, which describe the evolution of…
Stochastic evolution equations with compensated Poisson noise are considered in the variational approach with monotone and coercive coefficients. Here the Poisson noise is assumed to be time-homogeneous with $\sigma$-finite intensity…
Stationary solutions to a Fokker-Planck equation corresponding to a noisy logistic equation with correlated Gaussian white noises are constructed. Stationary distributions exist even if the corresponding deterministic system displays an…
We consider the Cauchy problem for a stochastic scalar parabolic-hyperbolic equation in any space dimension with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are nonlocal because they involve fractional…