On the study of a class of variational inequalities via Leray-Schauder degree.
On the tangential velocity arising in a crystalline approximation of evolving plane curves
In a crystalline algorithm, a tangential velocity is used implicitly. In this short note, it is specified for the case of evolving plane curves, and is characterized by using the intrinsic heat equation.
On the temperature distribution in cold ice
The linear heat equation predicts that the variations of temperature along a cold ice sheet {i.e. at a temperature less than is freezing point) due to a sudden increase in air temperature, are very very slow. Based on this we represent the nonlinear evolution of an ice sheet as a sequence of steady states. As a first fundamental indication that this model is correct well posedness with respect to the variations of initial and boundary data is proved. Further an estimate of the error made in evaluating...
On the time periodic free boundary associated to some nonlinear parabolic equations.
On the uniform boundedness of the solutions of systems of reaction-diffusion equations.
On the unique solvability of a nonlocal phase separation problem for multicomponent systems
A nonlocal model of phase separation in multicomponent systems is presented. It is derived from conservation principles and minimization of free energy containing a nonlocal part due to particle interaction. In contrast to the classical Cahn-Hilliard theory with higher order terms this leads to an evolution system of second order parabolic equations for the particle densities, coupled by nonlinear and nonlocal drift terms, and state equations which involve both chemical and interaction potential...
On the vanishing viscosity method for first order differential-functional IBVP
We consider the initial-boundary value problem for first order differential-functional equations. We present the `vanishing viscosity' method in order to obtain viscosity solutions. Our formulation includes problems with a retarded and deviated argument and differential-integral equations.
On the viscous Allen-Cahn and Cahn-Hilliard systems with Willmore regularization
We consider the viscous Allen-Cahn and Cahn-Hilliard models with an additional term called the nonlinear Willmore regularization. First, we are interested in the well-posedness of these two models. Furthermore, we prove that both models possess a global attractor. In addition, as far as the viscous Allen-Cahn equation is concerned, we construct a robust family of exponential attractors, i.e. attractors which are continuous with respect to the perturbation parameter. Finally, we give some numerical...
On the viscous Burgers equation in unbounded domain.
On the volume of intersection of three independent Wiener sausages
Let K be a compact, non-polar set in ℝm, m≥3 and let SKi(t)={Bi(s)+y: 0≤s≤t, y∈K} be Wiener sausages associated to independent brownian motions Bi, i=1, 2, 3 starting at 0. The expectation of volume of ⋂i=13SKi(t) with respect to product measure is obtained in terms of the equilibrium measure of K in the limit of large t.
On the weak solution of a three-point boundary value problem for a class of parabolic equations with energy specification.
On the wellposed singular boundary value problems for heat operator
On the well-posedness of the heat equation on unbounded domains.
On three-point boundary value problem with a weighted integral condition for a class of singular parabolic equations.
On uniqueness and existence of entropy solutions of weakly coupled systems of nonlinear degenerate parabolic equations.
On uniqueness and nonuniqueness of the positive Cauchy problem for parabolic equations with unbounded coefficients.
On uniqueness for a system of heat equations coupled in the boundary conditions.
On viscosity solutions for nontotally parabolic fully nonlinear equations
Opérateurs Paraboliques Dans Le Calcul Opérationnel Des Distributions A Support Dans Rn+ n ≥ 1
Operational Methods in the Environment of a Computer Algebra System
This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.The presented research is related to the operational calculus approach and its representative applications. Operational methods are considered, as well as their...