Nonlinear hyperbolic equations with dissipative temporal and spatial non-local memory.
Nonlinear perturbation of balayage spaces.
Nonlocal problem for the hyperbolic system of differential equation of the first order.
Nonlocal quadratic evolution problems
Nonlinear nonlocal parabolic equations modeling the evolution of density of mutually interacting particles are considered. The inertial type nonlinearity is quadratic and nonlocal while the diffusive term, also nonlocal, is anomalous and fractal, i.e., represented by a fractional power of the Laplacian. Conditions for global in time existence versus finite time blow-up are studied. Self-similar solutions are constructed for certain homogeneous initial data. Monte Carlo approximation schemes by interacting...
Non-simultaneous blow-up for a semilinear parabolic system with nonlinear memory.
Nonsmoothing in a single conservation law with memory.
Non-standard applications of the Łojasiewicz-Simon theory: Stabilization to equilibria of solutions to phase-field models
This is a survey of results on the long-time behavior of solutions to phase-field models and related problems. The central idea is based on several non-standard applications of the Łojasiewicz-Simon theory.
Nouveaux algorithmes performants en théorie du transport
Null controllability of a coupled model in population dynamics
We are concerned with the null controllability of a linear coupled population dynamics system or the so-called prey-predator model with Holling type I functional response of predator wherein both equations are structured in age and space. It is worth mentioning that in our case, the space variable is viewed as the “gene type” of population. The studied system is with two different dispersion coefficients which depend on the gene type variable and degenerate in the boundary. This system will be governed...
Numerical analysis of the two-dimensional thermo-diffusive model for flame propagation
Numerical Analysis of the Weighted Particle Method Applied to the Semiconductor Boltzmann Equation.
Numerical computation of a nonlocal double obstacle problem.
Numerical solution of a parabolic equation with a weakly singular positive-type memory term.
On a Caginalp phase-field system with a logarithmic nonlinearity
We consider a phase field system based on the Maxwell Cattaneo heat conduction law, with a logarithmic nonlinearity, associated with Dirichlet boundary conditions. In particular, we prove, in one and two space dimensions, the existence of a solution which is strictly separated from the singularities of the nonlinear term and that the problem possesses a finite-dimensional global attractor in terms of exponential attractors.
On a certain non-linear initial-boundary value problem for integro-differential equations of parabolic type
On a class of diffeomorphisms defined by integro-differential operators
We study an integro-differential operator Φ: H̅¹ → L² of Fredholm type and give sufficient conditions for Φ to be a diffeomorphism. An application to functional equations is presented.
On a class of parabolic integro-differential equations.
On a Fokker-Planck equation arising in population dynamics.
On a generalized retarded integral inequality with two variables.
On a parabolic integrodifferential equation of Barbashin type
In the present paper we study some basic qualitative properties of solutions of a nonlinear parabolic integrodifferential equation of Barbashin type which occurs frequently in applications. The fundamental integral inequality with explicit estimate is used to establish the results.