132 research outputs found
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 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
Convergence of the regularized short pulse equation to the short pulse one
We consider the regularized short-pulse equation, which contains nonlinear
dis- persive effects. We prove that as the diffusion parameter tends to zero,
the solutions of the dispersive equation converge to discontinuous weak
solutions of the short-pulse one. The proof relies on deriving suitable a
priori estimates together with an application of the compensated compactness
method in the Lp setting
Oleinik type estimates for the Ostrovsky-Hunter eequation
The Ostrovsky-Hunter equation provides a model for small-amplitude long waves
in a rotating fluid of finite depth. It is a nonlinear evolution equation. In
this paper we study the well-posedness for the Cauchy problem associated to
this equation within a class of bounded discontinuous solutions. We show that
we can replace the Kruzkov-type entropy inequalities by an Oleinik-type
estimate and prove uniqueness via a nonlocal adjoint problem. An implication is
that a shock wave in an entropy weak solution to the Ostrovsky-Hunter equation
is admissible only if it jumps down in value (like the inviscid Burgers
equation)
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