相关论文: The modified Klein Gordon equation for neolithic p…
We consider long time evolution of small solutions to general multispeed Klein-Gordon systems in 3+1 dimensions. We prove that such solutions are always global and scatter to a linear flow, thus extending previous partial results. The main…
Standard diffusion equation is based on Brownian motion of the dispersing species without considering persistence in the movement of the individuals. This description allows for the instantaneous spreading of the transported species over an…
The classical one-phase Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase transition, such as ice melting to water. This is accomplished by solving the heat equation on a time-dependent domain…
This paper presents an existence result for the anisotropic Cahn--Hilliard equation characterized by a potentially concentration-dependent degenerate mobility taking into account an anisotropic energy. The model allows for the degeneracy of…
A nonlinear theory of quantum Brownian motion in classical environment is developed based on a thermodynamically enhanced nonlinear Schrodinger equation. The latter is transformed via the Madelung transformation into a nonlinear quantum…
The Lotka-Euler equation is a mathematical expression used to study population dynamics and growth, particularly in the context of demography and ecology. The growth rate $\lambda$ is the speed at which an individual produce their…
A numerical method based on the hybridizable discontinuous Galerkin method in space and backward Euler in time is formulated and analyzed for solving the miscible displacement problem. Under low regularity assumptions, convergence is…
In this paper we investigate the Klein-Gordon equation in the past causal domain of a De Sitter brane imbedded in a Anti-de Sitter bulk. We solve the global mixed hyperbolic problem. We prove that any finite energy solution can be expressed…
We consider the asymptotic behavior of small global-in-time solutions to a 1D Klein-Gordon equation with a spatially localized, variable coefficient quadratic nonlinearity and a non-generic linear potential. The purpose of this work is to…
Recent experimental and theoretical works have shown that giant fluctuations are present during diffusion in liquid systems. We use linearized fluctuating hydrodynamics to calculate the net mass transfer due to these non equilibrium…
A generalised phase-space kinetic Boltzmann equation for highly non-equilibrium charged particle transport via localised and delocalised states is used to develop continuity, momentum and energy balance equations, accounting explicitly for…
We propose and study the evolving neural network (ENN) method for solving one-dimensional scalar hyperbolic conservation laws with linear and quadratic spatial fluxes. The ENN method first represents the initial data and the inflow boundary…
We present a review of our recent works directed towards discovery of a periodic, kink-like and soliton-like travelling wave solutions within the models of transport phenomena and the mathematical biology. Analytical description of these…
For the multi-mode Dicke model in a transport setting that exhibits collective boson transmissions, we construct the equation of motion for the cumulant generating function. Approximating the exact system of equations at the level of…
The FKPP equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a…
The mass transfer of interstitial impurities in a crystalline lattice under the influence of the fast-moving deformation disturbance of the type of a shock wave is considered. The velocity of the movement of the disturbance is supposed to…
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg…
In this paper we study some mathematical models describing evolution of population density and spread of epidemics in population systems in which spatial movement of individuals depends only on the departure and arrival locations and does…
This paper deals with the numerical (finite volume) approximation of reaction-diffusion systems with relaxation, among which the hyperbolic extension of the Allen--Cahn equation represents a notable prototype. Appropriate discretizations…
The aim of this paper is to study the metastable properties of the solutions to a hyperbolic relaxation of the classic Cahn-Hilliard equation in one space dimension, subject to either Neumann or Dirichlet boundary conditions. To perform…