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.
On the exponential growth of solutions to nonlinear hyperbolic equations.
On the extinction of the solution for an elliptic equation in a cylindrical domain
On the -convergence of Morrey operators
Following Morrey [14] we associate to any measurable symmetric matrix valued function such that
On the Generalized Korteweg-De Vries Equation.
On the Ginzburg-Landau energy with weight
On the homogenization of some nonlinear problems in perforated domains
On the instability of solitary-wave solutions for fifth-order water wave models.
On the instantaneous spreading for the Navier–Stokes system in the whole space
We consider the spatial behavior of the velocity field of a fluid filling the whole space () for arbitrarily small values of the time variable. We improve previous results on the spatial spreading by deducing the necessary conditions under more general assumptions on the localization of . We also give some new examples of solutions which have a stronger spatial localization than in the generic case.
On the Instantaneous Spreading for the Navier–Stokes System in the Whole Space
We consider the spatial behavior of the velocity field u(x, t) of a fluid filling the whole space () for arbitrarily small values of the time variable. We improve previous results on the spatial spreading by deducing the necessary conditions under more general assumptions on the localization of u. We also give some new examples of solutions which have a stronger spatial localization than in the generic case.
On the limit amplitude principle for a layer.
On the long time behavior of KdV type equations
In a series of recent papers, Martel and Merle solved the long-standing open problem on the existence of blow up solutions in the energy space for the critical generalized Korteweg- de Vries equation. Martel and Merle introduced new tools to study the nonlinear dynamics close to a solitary wave solution. The aim of the talk is to discuss the main ideas developed by Martel-Merle, together with a presentation of previously known closely related results.
On the long time behaviour of solutions of a class of autonomous reaction-diffusion systems.