Related papers: Group Analysis of Variable Coefficient Diffusion-C…
This article concerns second-order time discretization of subdiffusion equations with time-dependent diffusion coefficients. High-order differentiability and regularity estimates are established for subdiffusion equations with…
We consider birational projective contractions f:X -> Y from a smooth symplectic variety X over the complex numbers. We first show that exceptional rational curves on X deform in a family of dimension at least 2n-2. Then we show that these…
Time-fractional telegraph equations provide fundamental mathematical models for transport processes that exhibit memory and nonlocal effects in industrial and physical systems. These models arise naturally in heat transport in materials…
We study a second order scheme for spatial fractional differential equations with variable coefficients. Previous results mainly concentrate on equations with diffusion coefficients that are proportional to each other. In this paper, by…
We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…
Q-conditional symmetries (nonclassical symmetries) for a general class of two-component reaction-diffusion systems with non-constant diffusivities are studied. The work is a natural continuation of our paper (Cherniha and Davydovych, 2012)…
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…
Diffusion processes with boundaries are models of transport phenomena with wide applicability across many fields. These processes are described by their probability density functions (PDFs), which often obey Fokker-Planck equations (FPEs).…
We discuss a variety of codimension-one, non-invertible topological defects in general 3+1d QFTs with a discrete one-form global symmetry. These include condensation defects from higher gauging of the one-form symmetries on a…
In this report we obtain higher order asymptotic expansions of solutions to wave equations with frictional and viscoelastic damping terms. Although the diffusion phenomena are dominant, differences between the solutions we deal with and…
In this work, we consider an advection-diffusion equation, coupled to a Poisson equation for the velocity field. This type of coupling is typically encountered in models arising from plasma physics or porous media flow. The aim of this work…
The vortex-like solutions are studied in the framework of the gauge model of disclinations in elastic continuum. A complete set of model equations with disclination driven dislocations taken into account is considered. Within the linear…
The paper is devoted to a comprehensive second-order study of a remarkable class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to…
74J30The maximal group of Lie point symmetries of a system of nonlinear equations used in geophysical fluid dynamics is presented. The Lie algebra of this group is infinite-dimensional and involves three arbitrary functions of time. The…
We are interested in the numerical solution of nonsymmetric linear systems arising from the discretization of convection-diffusion partial differential equations with separable coefficients and dominant convection. Preconditioners based on…
This work presents an overview of several nonlinear reduction strategies for data compression from various research fields, and a comparison of their performance when applied to problems characterized by diffusion and/or advection terms. We…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
We perform complete group classification of the general class of quasi linear wave equations in two variables. This class may be seen as a broad generalization of the nonlinear d'Alembert, Liouville, sin/sinh-Gordon and Tzitzeica equations.…
The Lie point symmetries and corresponding invariant solutions are obtained for a Gaussian, irrotational, compressible fluid flow. A supersymmetric extension of this model is then formulated through the use of a superspace and superfield…
This paper presents a model of van der Waals forces in the framework of diffusion-convection equations. The model consists of a nonlinear and degenerated diffusion-convection equation, which furthermore can be considered as a model for slow…