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We consider solvability of the generalized reaction-diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction-diffusion…
In this article, a special static spherically symmetric perfect fluid solution of Einstein's equations is provided. Though pressure and density both diverge at the origin, their ratio remains constant. The solution presented here fails to…
Researchers have employed variations of the Smoluchowski coagulation equation to model a wide variety of both organic and inorganic phenomena and with relatively few known analytical solutions, numerical solutions play an important role in…
We consider a large number of randomly dispersed spherical, identical, perfectly conducting inclusions (of infinite conductivity) in a bounded domain. The host medium's conductivity is finite and can be inhomogeneous. In the dilute limit,…
We study the problem of homogenization for inertial particles moving in a time dependent random velocity field and subject to molecular diffusion. We show that, under appropriate assumptions on the velocity field, the large--scale,…
Based upon the intrinsic symmetries approach to inhomogeneous cosmologies, we propose an exact solution to Einstein's field equations where the spatial sections are flat and the source is a non-perfect fluid such that the dissipative terms…
This work studies a simplified model of the gravitational instability of an initially homogeneous infinite medium, represented by $\TT^d$, based on the approximation that the mean fluid velocity is always proportional to the local…
A simple manner to describe the diffusive relaxation of a colloidal fluid adsorbed in a porous medium is to model the porous medium as a set of spherical particles fixed in space at random positions with prescribed statistical structural…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
This paper studies the solutions of a reaction--diffusion system with nonlinearities that generalise the Lengyel--Epstein and FitzHugh--Nagumo nonlinearities. Sufficient conditions are derived for the global asymptotic stability of the…
A uniform approach is introduced to study the existence of measure valued solutions to the homogeneous Boltzmann equation for both hard potential with finite energy, and soft potential with finite or infinite energy, by using Toscani…
This work is devoted to the derivation and the matematical study of a new model for water-soluble polymers and metal ions interactions, which are used in chemistry for their wide range of applications. First, we motivate and derive a model…
We propose an alternative method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized…
We prove stability results for nonlinear diffusion equations of the porous medium and fast diffusion types with respect to the nonlinearity power $m$: solutions with fixed data converge in a suitable sense to the solution of the limit…
We construct exact static inhomogeneous solutions to Einstein's equations with counter flow of particle fluid and a positive cosmological constant by using the Sasaki metrics on three-dimensional spaces. The solutions, which admit an…
We suggest a new approach for describing quantum dissipation in a small systems for which the system-plus-reservoir approach is not relevant. We first analyze the fact that equilibrium thermodynamics may reveal the existence of an…
In this paper, we prove a uniqueness result in the inverse problem of determining several non-constant coefficients of one-dimensional reaction-diffusion equations. Such reaction-diffusion equations include the classical model of…
The spatially homogeneous Boltzmann equation with hard potentials is considered for measure valued initial data having finite mass and energy. We prove the existence of \emph{weak measure solutions}, with and without angular cutoff on the…
Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the…
Convection-diffusion equations provide the basis for describing heat and mass transfer phenomena as well as processes of continuum mechanics. To handle flows in porous media, the fundamental issue is to model correctly the convective…