Related papers: Existence of Strong Solution for the Complexified …
Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift are considered. We do not impose coercivity conditions on coefficients. A novel method of proof for establishing existence and…
We prove existence and uniqueness for some nonlinear stochastic differential equation used in molecular dynamics, whose nonlinearity comes from a conditional expectation term. We also introduce an interacting particle system in order to…
The nonlinear Schr\"odinger equation (NLSE) models the slowly varying envelope dynamics of a weakly nonlinear quasi-monochromatic wave packet in dispersive media. In the context of Bose-Einstein condensate (BEC), it is often referred to as…
In this paper, we study existence and uniqueness to multidimensional Reflected Backward Stochastic Differential Equation in an open convex domain, allowing for oblique directions of reflection. In a Markovian framework, combining \emph{a…
In this paper we establish local and global existence and uniqueness of solutions for general nonlinear evolution equations with coefficients satisfying some local monotonicity and generalized coercivity conditions. An analogous result is…
In this paper, we announce a rigorous approach to establishing uniqueness results, under certain conditions, for initial-boundary-value problems for a class of linear evolution partial differential equations (PDEs) formulated in a…
Regularity of the Boltzmann equation, particularly in the presence of physical boundary conditions, heavily relies on the geometry of the boundaries. In the case of non-convex domains with specular reflection boundary conditions, the…
In this paper, we prove the existence of multiple solutions for a nonlinear nonlocal elliptic PDE involving a singularity which is given as \begin{eqnarray} (-\Delta_p)^s u&=& \frac{\lambda}{u^\gamma}+u^q~\text{in}~\Omega,\nonumber…
The existence of stationary distributions in a multicomponent Boltzmann equation using a non-additive kinetic energy composition rule for binary collisions is discussed. It is found that detailed balance is not achieved when -- in contrast…
We prove existence and uniqueness results for nonlinear third order partial differential equations of the form $$ f_t - f_{yyy} = \sum_{j=0}^3 b_j (y, t; f) ~f^{(j)} + r(y, t) $$ where superscript $j$ denotes the $j$-th partial derivative…
The Poisson-Boltzmann (PB) equation provides a mean-field theory of electrolyte solutions at interfaces and in confinement, describing how ions reorganize close to charged surfaces to form the so-called electrical double layer (EDL), with…
The Bose-Einstein condensate (BEC), confined in a combination of the cigar-shaped trap and axial optical lattice, is studied in the framework of two models described by two versions of the one-dimensional (1D) discrete nonpolynomial…
In this work a dynamical system approach is taken to systematically investigate the one-dimensional classical Poisson-Boltzmann (PB) equation with various boundary conditions. This framework, particularly, the phase space portrait, has a…
We investigate a Poisson-Nernst-Planck type system in three spatial dimensions where the strength of the electric drift depends on a possibly small parameter and the particles are assumed to diffuse quadratically. On grounds of the global…
The Landau--Lifshitz--Baryakhtar (LLBar) equation perturbed by both additive and multiplicative noises is a system of fourth order stochastic PDEs which models the evolution of magnetic spin fields in ferromagnetic materials at elevated…
We prove existence and uniqueness of solutions of a large class of initial-boundary-value problems characterized by a quasi-linear third order equation (the third order term being dissipative) on a finite space interval with Dirichlet,…
We present a continuous finite element method for some examples of fully nonlinear elliptic equation. A key tool is the discretisation proposed in Lakkis & Pryer (2011, SISC) allowing us to work directly on the strong form of a linear PDE.…
In this paper we consider a one-dimensional non-linear Schroedinger equation (NLSE) with a periodic potential. In the semiclassical limit we prove that the stationary solutions of the Bose-Hubbard equation approximate the stationary…
We generalize the notion of pathwise viscosity solutions, put forward by Lions and Souganidis to study fully nonlinear stochastic partial differential equations, to equations set on a sub-domain with Neumann boundary conditions. Under a…
Piezoelectric appliances have become hugely important in the past century and computer simulations play an essential part in the modern design process thereof. While much work has been invested into the practical simulation of piezoelectric…