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5 papers · 2 filters
Attractors for nonlinear reaction-diffusion systems in unbounded domains via the method of short trajectories
Maurizio Grasselli, Dalibor Pražák, Giulio Schimperna
We consider a nonlinear reaction-diffusion equation settled on the whole euclidean space. We prove the well-posedness of the corresponding Cauchy problem in a general functional se…
Trajectory and smooth attractors for Cahn-Hilliard equations with inertial term
Maurizio Grasselli, Giulio Schimperna, Sergey Zelik
The paper is devoted to a modification of the classical Cahn-Hilliard equation proposed by some physicists. This modification is obtained by adding the second time derivative of th…
estimates for the eigenfunctions corresponding to real eigenvalues of the Tricomi operator
Alberto Favaron
We introduce a family of normal Tricomi domains $\Om_{\a,\b}$, $\a>0>\b$, and we show that its elements are -star-shaped with respect to the vector field $D=-3x\parti…
An H^1 setting for the Navier-Stokes equations: quantitative estimates
Carlo Morosi, Livio Pizzocchero
We consider the incompressible Navier-Stokes (NS) equations on a torus, in the setting of the spaces L^2 and H^1; our approach is based on a general framework for semi- or quasi-li…
Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities
Matteo Bonforte, Jean Dolbeault, Gabriele Grillo +1
The goal of this note is to state the optimal decay rate for solutions of the nonlinear fast diffusion equation and, in self-similar variables, the optimal convergence rates to Bar…