Radial symmetric solutions of the Cahn-Hilliard equation with degenerate mobility.
Radially symmetric solutions of a chemotaxis model in the plane-the supercritical case
The existence, uniqueness and large time behaviour of radially symmetric solutions to a chemotaxis system in the plane ℝ² are studied for the (supercritical) value of mass greater than 8π.
Radiative Heating of a Glass Plate
This paper aims to prove existence and uniqueness of a solution to the coupling of a nonlinear heat equation with nonlinear boundary conditions with the exact radiative transfer equation, assuming the absorption coefficient to be piecewise constant and null for small values of the wavelength as in the paper of N. Siedow, T. Grosan, D. Lochegnies, E. Romero, “Application of a New Method for Radiative Heat Tranfer to Flat Glass Tempering”, J. Am. Ceram. Soc., 88(8):2181-2187 (2005). An important...
Random attractors for stochastic two-compartment Gray-Scott equations with a multiplicative noise
In this paper, we consider the existence of a pullback attractor for the random dynamical system generated by stochastic two-compartment Gray-Scott equation for a multiplicative noise with the homogeneous Neumann boundary condition on a bounded domain of space dimension n ≤ 3. We first show that the stochastic Gray-Scott equation generates a random dynamical system by transforming this stochastic equation into a random one. We also show that the existence of a random attractor for the stochastic...
Rarefaction waves in nonlocal convection-diffusion equations
We consider a nonlocal convection-diffusion equation , where J is a probability density. We supplement this equation with step-like initial conditions and prove the convergence of the corresponding solutions towards a rarefaction wave, i.e. a unique entropy solution of the Riemann problem for the inviscid Burgers equation.
Rate of approach to a singular steady state in quasilinear reaction-diffusion equations
Rate of convergence of finite-difference approximations for degenerate linear parabolic equations with and coefficients.
Reaction diffusion equations and quadratic convergence.
Reaction-diffusion in nonsmooth and closed domains.
Reaction-diffusion problems in cylinders with no invariance by translation. Part II : monotone perturbations
Reaction-diffusion system of equations in non-stationary medium and arbitrary non-smooth domains.
Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions.
Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions
Sufficient conditions for destabilizing effects of certain unilateral boundary conditions and for the existence of bifurcation points for spatial patterns to reaction-diffusion systems of the activator-inhibitor type are proved. The conditions are related with the mollification method employed to overcome difficulties connected with empty interiors of appropriate convex cones.
Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions II, Examples
The destabilizing effect of four different types of multivalued conditions describing the influence of semipermeable membranes or of unilateral inner sources to the reaction-diffusion system is investigated. The validity of the assumptions sufficient for the destabilization which were stated in the first part is verified for these cases. Thus the existence of points at which the spatial patterns bifurcate from trivial solutions is proved.
Reaction-diffusion systems: stabilizing effect of conditions described by quasivariational inequalities
Reaction-diffusion systems are studied under the assumptions guaranteeing diffusion driven instability and arising of spatial patterns. A stabilizing influence of unilateral conditions given by quasivariational inequalities to this effect is described.
Reaction-diffusion systems with 1-homogeneous non-linearity.
Reaction-diffusion systems with prescribed large time behaviour
Reaction-diffusion systems with time delays: monotonicity, invariance, comparison and convergence.
Reaction-diffusion-convection problems in unbounded cylinders.
The work is devoted to reaction-diffusion-convection problems in unbounded cylinders. We study the Fredholm property and properness of the corresponding elliptic operators and define the topological degree. Together with analysis of the spectrum of the linearized operators it allows us to study bifurcations of solutions, to prove existence of convective waves, and to make some conclusions about their stability.
Reaction-Difusion Model of Early Carcinogenesis: The Effects of Influx of Mutated Cells
In this paper we explore a new model of field carcinogenesis, inspired by lung cancer precursor lesions, which includes dynamics of a spatially distributed population of pre-cancerous cells c(t, x), constantly supplied by an influx μ of mutated normal cells. Cell proliferation is controlled by growth factor molecules bound to cells, b(t, x). Free growth factor molecules g(t, x) are produced by precancerous cells and may diffuse before they become bound to other cells. The purpose of modelling is...