On the Chaplighin method for partial differential equations of the first order
On the convergence of numerical schemes for the Boltzmann equation
On the Dirichlet problem for a second order elliptic system with degeneration on the entire domain boundary.
On the existence and uniqueness of solutions of some partial differential functional equations
On the existence and uniqueness of solutions of the Darboux problem for partial differential-functional equations in a Banach space
On the existence of weak solutions of perturbated systems with critical growth.
On the Landau approximation in plasma physics
On the non-convergence of successive approximations in the Darboux problem for the equation
On the nonconvergence of successive approximations in the theory of the equation
On the -growth of entire function solutions of Helmholtz equation.
On the relation between the Maslov-Whitham method and the weak asymptotics method
We explain the relation between the weak asymptotics method introduced by the author and V. M. Shelkovich and the classical Maslov-Whitham method for constructing approximate solutions describing the propagation of nonlinear solitary waves.
On the structure of layers for singularly perturbed equations in the case of unbounded energy
We consider singular perturbation variational problems depending on a small parameter . The right hand side is such that the energy does not remain bounded as . The asymptotic behavior involves internal layers where most of the energy concentrates. Three examples are addressed, with limits elliptic, parabolic and hyperbolic respectively, whereas the problems with are elliptic. In the parabolic and hyperbolic cases, the propagation of singularities appear as an integral property after integrating...
On the structure of layers for singularly perturbed equations in the case of unbounded energy
We consider singular perturbation variational problems depending on a small parameter ε. The right hand side is such that the energy does not remain bounded as ε → 0. The asymptotic behavior involves internal layers where most of the energy concentrates. Three examples are addressed, with limits elliptic, parabolic and hyperbolic respectively, whereas the problems with ε > 0 are elliptic. In the parabolic and hyperbolic cases, the propagation of singularities appear as an integral property after...
On the Uniqueness of Solutions and on the Convergence of Successive Approximations for Certain Initial Problems of Equations of the Higher Orders
On the uniqueness of solutions and the convergence of successive approximations in the Darboux problem for certain differential equations of the type
One iterative method concerning the solution of Dirichlet's problem
Parabolic partial differential equations with memory
Parameter shifting and complete families of solutions to a singular parabolic equation
Parareal operator splitting techniques for multi-scale reaction waves: Numerical analysis and strategies
In this paper, we investigate the coupling between operator splitting techniques and a time parallelization scheme, the parareal algorithm, as a numerical strategy for the simulation of reaction-diffusion equations modelling multi-scale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reactive...
Parareal operator splitting techniques for multi-scale reaction waves: Numerical analysis and strategies
In this paper, we investigate the coupling between operator splitting techniques and a time parallelization scheme, the parareal algorithm, as a numerical strategy for the simulation of reaction-diffusion equations modelling multi-scale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reactive...