Related papers: Mathematical analysis of a one-dimensional model f…
In this paper we present numerical methods - finite differences and finite elements - for solution of partial differential equation of fractional order in time for one-dimensional space. This equation describes anomalous diffusion which is…
Ageing in systems without detailed balance is studied in bosonic contact and pair-contact processes with Levy diffusion. In the ageing regime, the dynamical scaling of the two-time correlation function and two-time response function is…
The fluid models mentioned in the title are studied in a modified approach, based on two formulas for the mass function. All characteristics of the fluid are expressed through a master potential, satisfying an ordinary second order…
Nonlinear waves in a liquid with gas bubbles are studied. Higher order terms with respect to the small parameter are taken into account in the derivation of the equation for nonlinear waves. A nonlinear differential equation is derived for…
Partial differential equations are a convenient way to describe reaction- advection-diffusion processes of signalling models. If only one cell type is present, and tissue dynamics can be neglected, the equations can be solved directly.…
Recent studies on the phenomenology of ageing in certain many-particle systems which are at a critical point of their non-equilibrium steady-states, are reviewed. Examples include the contact process, the parity-conserving…
This study handles spatial three-dimensional solution of the nonlinear diffusion equation without particular initial conditions. The functional behavior of the equation and the concentration have been studied in new ways. An auxiliary…
The flow of power law fluids, which include shear thinning and shear thickening as well as Newtonian as a special case, in networks of interconnected elastic tubes is investigated using a residual based pore scale network modeling method…
We consider a system of partial differential equations describing the steady flow of a compressible heat conducting Newtonian fluid in a three-dimensional channel with inflow and outflow part. We show the existence of a strong solution…
A nonlinear partial differential equation is a nonlinear relationship between an unknown function and how it changes due to two or more input variables. A numerical method reduces such an equation to arithmetic for quick visualization, but…
This paper studies the upper and lower bounds of the lifespan for the classical solutions to the initial value problems of one dimensional wave equations with non-autonomous semilinear terms including the space-derivative of the unknown…
System of semilinear ordinary differential equation and fractional differential equation of distributed order is investigated and solved in a mild and classical sense. Such a system arises as a distributed derivative model of…
We prove regularity estimates for time derivatives of a large class of nonlinear parabolic partial differential systems. This includes the instationary (symmetric) p-Laplace system and models for non Newtonien fluids of powerlaw or Carreau…
Motivated by numerically modeling surface waves for inviscid Euler equations, we analyze linear models for damped water waves and establish decay properties for the energy for sufficiently regular initial configurations. Our findings give…
In this paper, we begin by reviewing a certain number of mathematical challenges posed by the modelling of collective dynamics and self-organization. Then, we focus on two specific problems, first, the derivation of fluid equations from…
In this paper, we overview the recent progresses on the lifespan estimates of classical solutions of the initial value problems for nonlinear wave equations in one space dimension. There are mainly two directions of the developments on the…
The gradual accumulation of damage and dysregulation during the aging of living organisms can be quantified. Even so, the aging process is complex and has multiple interacting physiological scales -- from the molecular to cellular to whole…
We analyse the underlying nonlinear partial differential equation which arises in the study of gravitating flat fluid plates of embedding class one. Our interest in this equation lies in discussing new solutions that can be found by means…
We study a class of one-dimensional classical fluids with penetrable particles interacting through positive, purely repulsive, pair-potentials. Starting from some lower bounds to the total potential energy, we draw results on the…
In this paper are examined general classes of linear and non-linear analytical systems of partial differential equations. Indeed the integrability conditions are found and if they are satisfied, the solutions are given as functional series…