An Interior Estimate for a Nonlinear Parabolic Equation

In this paper there are estimated the derivatives of the solution of an initial boundary value problem for a nonlinear uniformly parabolic equation in the interior with the total variation of the boundary data and the L^{infinity}-norm of the initial condition.Comment: 16 page

Solitary waves for Maxwell-Schrodinger equations

In this paper we study the solitary waves for the coupled Schr\"odinger - Maxwell equations in three-dimensional space. We prove the existence of a sequence of radial solitary waves for these equations with a fixed $L^2$ norm. We study the asymptotic behavior and the smoothness of these solutions. We show also the fact that the eigenvalues are negative and the first one is isolated.Comment: 31 page

On the Boundary Control of Systems of Conservation Laws

The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand, we give an example showing that exact controllability in finite time cannot be achieved, in general.Comment: 16 pages, 5figure

Convergence of the Ostrovsky equation to the Ostrovsky-Hunter one

We consider the Ostrovsky equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tend to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the Ostrovsky-Hunter equation. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the L^p setting

Wellposedness results for the short pulse equation

The short pulse equation provides a model for the propagation of ultra-short light pulses in silica optical fibers. It is a nonlinear evolution equation. In this paper the wellposedness of bounded solutions for the homogeneous initial boundary value problem and the Cauchy problem associated to this equation are studied.Comment: arXiv admin note: text overlap with arXiv:1310.701