On the behaviour of solutions to the nonlinear elliptic Neumann problem in unbounded domains
The asymptotic behaviour is studied for minima of regular variational problems with Neumann boundary conditions on noncompact part of boundary.
On the blow up phenomenon for the critical nonlinear Schrödinger equation in 1D
On the blowing up of solutions to nonlinear wave equations in two space dimensions.
On the blowup of multidimensional semilinear heat equations
On the blowup theory for the critical nonlinear Schrödinger equations
On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions
On the Caginalp system with dynamic boundary conditions and singular potentials
This article is devoted to the study of the Caginalp phase field system with dynamic boundary conditions and singular potentials. We first show that, for initial data in , the solutions are strictly separated from the singularities of the potential. This turns out to be our main argument in the proof of the existence and uniqueness of solutions. We then prove the existence of global attractors. In the last part of the article, we adapt well-known results concerning the Łojasiewicz inequality in...
On the complex structure of positive solutions to Matukuma-type equations
On the Convective Cahn-Hilliard Equation
The author studies the convective Cahn-Hilliard equation. Some results on the existence of classical solutions and asymptotic behavior of solutions are established. The instability of the traveling waves is also discussed.
On the decay estimates for the wave equation with a local degenerate or nondegenerate dissipation.
On the Decay of Solutions of Some Nonlinear Dissipative Wave Equations in Higher Dimensions.
On the dimension of the pullback attractors for -Navier-Stokes equations.
On the dynamics of nonautonomous parabolic systems involving the Grushin operators.
On the dynamics of the characteristic curves for the LSW model.
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 energy critical focusing non-linear wave equation
On the enumerable set of different characteristic sets of solutions of a Pfaffian linear system.
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 of blowing-up solutions for a mean field equation
On the expansion of starshaped hypersurfaces by symmetric functions of their principal curvatures.