Derivation of models of compressible miscible displacement in partially fractured reservoirs.
Derivation of the Reynolds equation for lubrication of a rotating shaft
In this paper, using the asymptotic expansion, we prove that the Reynolds lubrication equation is an approximation of the full Navier–Stokes equations in thin gap between two coaxial cylinders in relative motion. Boundary layer correctors are computed. The error estimate in terms of domain thickness for the asymptotic expansion is given. The corrector for classical Reynolds approximation is computed.
Derivation of the Zakharov equations
Description of regional blow-up in a porous-medium equation.
Destabilization for quasivariational inequalities of reaction-diffusion type
We consider a reaction-diffusion system of the activator-inhibitor type with unilateral boundary conditions leading to a quasivariational inequality. We show that there exists a positive eigenvalue of the problem and we obtain an instability of the trivial solution also in some area of parameters where the trivial solution of the same system with Dirichlet and Neumann boundary conditions is stable. Theorems are proved using the method of a jump in the Leray-Schauder degree.
Destabilizing effect of unilateral conditions in reaction-diffusion systems
Detection of scales of heterogeneity and parabolic homogenization applying very weak multiscale convergence.
Deterministic homogenization of parabolic monotone operators with time dependent coefficients.
Deuxième microlocalisation simultanée et applications
Development of small and large compressive pulses in two-phase flow
The evolutions of small and large compressive pulses are studied in a two-phase flow of gas and dust particles with a variable azimuthal velocity. The method of relatively undistorted waves is used to study the mechanical pulses of different types in a rotational, axisymmetric dusty gas. The results obtained are compared with that of nonrotating medium. Asymptotic expansion procedure is used to discuss the nonlinear theory of geometrical acoustics. The influence of the solid particles and the rotational...
Die klassisch-reguläre Lösbarkeit des Rand-Anfangswertproblems nichtlinearer Wellengleichungen mit einer Randbedingung vom gemischten Typ.
Differentiability and growth of solutions of partial differential equations.
Differentiability and partial Hölder continuity of the solutions of non-linear elliptic systems of order with quadratic growth
Differential inequalities for a nonlinear partial differential equation of the fourth order
Differential inequalities of parabolic type in the Sobolev space
Differential-functional inequalities of parabolic type in unbounded regions
Diffraction by convex bodies
Diffusion and cross-diffusion in pattern formation
We discuss the stability and instability properties of steady state solutions to single equations, shadow systems, as well as systems. Our basic observation is that the more complicated the pattern are, the more unstable they tend to be.
Diffusion in long-range correlated Ornstein-Uhlenbeck flows.
Diffusion limit for the phenomenon of random genetic drift
The paper deals with mathematical modelling of population genetics processes. The formulated model describes the random genetic drift. The fluctuations of gene frequency in consecutive generations are described in terms of a random walk. The position of a moving particle is interpreted as the state of the population expressed as the frequency of appearance of a specific gene. This leads to a continuous model on the microscopic level in the form of two first order differential equations (known as...