On the dimension of the pullback attractors for -Navier-Stokes equations.
On the Dirac delta as initial condition for nonlinear Schrödinger equations
On the Dirichlet problem for a second order elliptic system with degeneration on the entire domain boundary.
On the Dirichlet problem for linear elliptic equations in plane domains with corners
On the Dirichlet problem for minimal graphs in hyperbolic space.
On the Dirichlet problem for quasilinear elliptic second order equations with triple degeneracy and singularity in a domain with a boundary conical point.
On the Dirichlet problem for the nonlinear wave equation in bounded domains with corner points.
On the discretization of a partial differential equation in the neighborhood of a periodic orbit.
On the domain dependence of solutions to the two-phase Stefan problem
We prove that solutions to the two-phase Stefan problem defined on a sequence of spatial domains converge to a solution of the same problem on a domain where is the limit of in the sense of Mosco. The corresponding free boundaries converge in the sense of Lebesgue measure on .
On the double-well problem for Dirac operators
On the dynamics of nonautonomous parabolic systems involving the Grushin operators.
On the dynamics of the characteristic curves for the LSW model.
On the effect of the domain geometry on uniqueness of positive solutions of
On the eigenfunction expansion method for semilinear dissipative equations in bounded domains and the Kuramoto-Sivashinsky equation in a ball
Presented herein is a method of constructing solutions of semilinear dissipative evolution equations in bounded domains. For small initial data this approach permits one to represent the solution in the form of an eigenfunction expansion series and to calculate the higher-order long-time asymptotics. It is applied to the spatially 3D Kuramoto-Sivashinsky equation in the unit ball B in the linearly stable case. A global-in-time mild solution is constructed in the space , s < 2, and the uniqueness...
On the elliptic problems involving multisingular inverse square potentials and concave-convex nonlinearities.
On the energy critical focusing non-linear wave equation
On the enumerable set of different characteristic sets of solutions of a Pfaffian linear system.
On the Euler equations of incompressible perfect fluids
On the existence and regularity of the solutions to the incompressible Navier-Stokes equations in presence of mass diffusion
This paper is devoted to the study of the incompressible Navier-Stokes equations with mass diffusion in a bounded domain in R³ with C³ boundary. We prove the existence of weak solutions, in the large, and the behavior of the solutions as the diffusion parameter λ → 0. Moreover, the existence of L²-strong solution, in the small, and in the large for small data, is proved. Asymptotic regularity (the regularity after a finite period) of a weak solution is studied. Finally, using the Dore-Venni theory,...
On the existence and smoothness of radially symmetric solutions of a BVP for a class of nonlinear, non-Lipschitz perturbations of the Laplace equation.