相关论文: A fast solver for systems of reaction-diffusion eq…

Under general conditions we show that the solution of a stochastic parabolic partial differential equation of the form \[ \partial_t u = \mathrm{div} (A \nabla u) + f(t,x, u) + g_i (t,x,u) \dot{w}^i_t \] is almost surely H\"older continuous…

As a generalization of deterministic, nonlinear conservative dynamical systems, a notion of {\em canonical conservative dynamics} with respect to a positive, differentiable stationary density $\rho(x)$ is introduced: $\dot{x}=j(x)$ in which…

In this article I present a fast and direct method for solving several types of linear finite difference equations (FDE) with constant coefficients. The method is based on a polynomial form of the translation operator and its inverse, and…

We consider the Fast Diffusion Equation $u_t=\Delta u^m$ posed in a bounded smooth domain $\Omega\subset \RR^d$ with homogeneous Dirichlet conditions; the exponent range is $m_s=(d-2)_+/(d+2)<m<1$. It is known that bounded positive…

High-dimensional fractional reaction-diffusion equations have numerous applications in the fields of biology, chemistry, and physics, and exhibit a range of rich phenomena. While classical algorithms have an exponential complexity in the…

The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $\alpha\in(0,1)$. After using quasi-boundary…

A novel global energy model for multi-class semantic image segmentation is proposed that admits very efficient exact inference and derivative calculations for learning. Inference in this model is equivalent to MAP inference in a particular…

We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…

We establish symmetrization results for the solutions of the linear fractional diffusion equation $\partial_t u +(-\Delta)^{\sigma/2}u=f$ and itselliptic counterpart $h v +(-\Delta)^{\sigma/2}v=f$, $h>0$, using the concept of comparison of…

Existence of specific \emph{eternal solutions} in exponential self-similar form to the following quasilinear diffusion equation with strong absorption$$\partial_t u=\Delta u^m-|x|^{\sigma}u^q,$$posed for…

Many important applications are available for nonlinear reaction-diffusion equation especially in the area of biology and engineering. Therefore a mathematical model for Lie symmetry reduction of system of nonlinear reaction-diffusion…

We study the following ultraparabolic equation \[ \frac{\partial}{\partial t}u\left(t,s\right)+\frac{\partial}{\partial…

We consider the drift-diffusion equation $u_t-\epsilon\Delta u + \nabla \cdot(u\nabla K^*u)=0$ in the whole space with global-in-time solutions bounded in all Sobolev spaces; for simplicity, we restrict ourselves to the model case…

The fast reaction limit for a nonlinear bulk-surface reaction-diffusion system is investigated. This system describes a reversible reaction with arbitrary stoichiometric coefficients, where one chemical is present in a bounded vessel…

We consider the asymptotic behaviour of positive solutions $u(t,x)$ of the fast diffusion equation $u_t=\Delta (u^{m}/m)={\rm div} (u^{m-1}\nabla u)$ posed for $x\in\RR^d$, $t>0$, with a precise value for the exponent $m=(d-4)/(d-2)$. The…

Partial differential equations are often used to model various physical phenomena, such as heat diffusion, wave propagation, fluid dynamics, elasticity, electrodynamics and image processing, and many analytic approaches or traditional…

In this paper we discuss numerical methods and algorithms for the solution of NLTE stellar atmosphere problems involving expanding atmospheres, e.g., found in novae, supernovae and stellar winds. We show how a scheme of nested iterations…

We investigate nonnegative solutions $u(x,t)$ and $v(x,t)$ of the nonlinear system of inequalities \[0\leq(\partial_t -\Delta)^\alpha u\leq v^\lambda\] \[ 0\leq (\partial_t -\Delta)^\beta v\leq u^\sigma\] in $\mathbb{R}^n \times\mathbb{R}$,…

This paper investigates the asymptotic behavior of the solutions of the Fisher-KPP equation in a heterogeneous medium, $$\partial_t u = \partial_{xx} u + f(x,u),$$ associated with a compactly supported initial datum. A typical nonlinearity…

In order to describe large transverse momentum ($p_T$) distributions observed in high energy nucleus-nucleus collisions, a stochastic model in the three dimensional rapidity space is introduced. The fundamental solution of the radial…