相关论文: A New Perturbative Technique for Solving Integro-P…
The work deals with the studies of the existence of solutions of an integro-differential equation in the situation of the difference of the standard Laplacian and the bi-Laplacian in the diffusion term. The proof of the existence of…
Evaluating the linear response of a driven system to a change in environment temperature(s) is essential for understanding thermal properties of nonequilibrium systems. The system is kept in weak contact with possibly different fast…
A kind of spatial fractional diffusion equations in this paper are studied. Firstly, an L1 formula is employed for the spatial discretization of the equations. Then, a second order scheme is derived based on the resulting semi-discrete…
Statistical systems with time-periodic spatially non-uniform forces are of immense importance in several areas of physics. In this paper, we provide an analytical expression of the time-periodic probability distribution function of…
The phenomenon of turbulent thermal diffusion in temperature-stratified turbulence causing a non-diffusive turbulent flux of inertial and non-inertial particles in the direction of the turbulent heat flux is found using direct numerical…
Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial…
Partial differential equations with distributional sources---in particular, involving (derivatives of) delta distributions---have become increasingly ubiquitous in numerous areas of physics and applied mathematics. It is often of…
Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori…
The numerical solution methods for partial differential equation (PDE) solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods…
In this paper we consider a class of fourth order nonlinear integro-differential equations with Navier boundary conditions. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…
In this paper we study some cases of time-fractional nonlinear dispersive equations (NDEs) involving Caputo derivatives, by means of the invariant subspace method. This method allows to find exact solutions to nonlinear time-fractional…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
Lie group method provides an efficient tool to solve a differential equation. This paper suggests a fractional partner for fractional partial differential equations using a fractional characteristic method. A space-time fractional diffusion…
In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In…
We generalize the method of obtaining the fundamental linear partial differential equations such as the diffusion and Schrodinger equation, Dirac and telegrapher's equation from a simple stochastic consideration to arrive at certain…
We study the problem of identifying unknown processes embedded in time-dependent partial differential equation (PDE) using observational data, with an application to advection-diffusion type PDE. We first conduct theoretical analysis and…
This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A…
We study the set of $T$-periodic solutions of a class of $T$-periodically perturbed Differential-Algebraic Equations, allowing the perturbation to contain a distributed and possibly infinite delay. Under suitable assumptions, the perturbed…
We address the problem of classification of integrable differential-difference equations in 2+1 dimensions with one/two discrete variables. Our approach is based on the method of hydrodynamic reductions and its generalisation to dispersive…
This paper considers one-dimensional heat transfer in a media with temperature-dependent thermal conductivity. To model the transient behavior of the system, we solve numerically the one-dimensional unsteady heat conduction equation with…