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ON DIFFERENTIABILITY OF SRB STATES FOR PARTIALLY HYPERBOLIC SYSTEMS
DIFFERENTIABILITY HYPERBOLIC SYSTEMS
2015/9/29
Consider a one parameter family of diffeomorphisms
fε such that f0 is an Anosov element in a standard abelian Anosov
action having sufficiently strong mixing properties. Let νε be any
u-...
We study the nature of the Nonlinear Schr\"odinger equation ground states on the product spaces $\R^n\times M^k$, where $M^k$ is a compact Riemannian manifold. We prove that for small $L^2$ masses the...
Semi-classical states for the Nonlinear Schroinger Equation on saddle points of the potential via variational methods
Nonlinear Schrodinger Equation Semiclassical states Variational Methods
2011/9/22
Abstract: In this paper we study semiclassical states for the problem $$ -\eps^2 \Delta u + V(x) u = f(u) \qquad \hbox{in} \RN,$$ where $f(u)$ is a superlinear nonlinear term. Under our hypotheses on ...
On asymptotic stability of moving ground states of the nonlinear Schrodinger equation
asymptotic stability nonlinear Schrodinger equation Analysis of PDEs
2011/9/20
Abstract: We extend to the case of moving solitons, the result on asymptotic stability of ground states of the NLS with a short range linear potential obtained by the author in a previous paper. Now w...
Stability of bound states of Hamiltonian PDEs in the degenerate cases
Hamiltonian PDEs degenerate cases Analysis of PDEs
2011/9/14
Abstract: We consider a Hamiltonian systems which is invariant under a one-parameter unitary group. We give a criterion for the stability and instability of bound states for the degenerate case. We ap...
Numerical Continuation of resonances and bound states in coupled channel Schrödinger equations
Resonances Numerical Continuation Coupled Channels Schr¨odinger equation
2011/1/17
In this contribution, we introduce numerical continuation methods and bifurcation theory, techniques which find their roots in the study of dynamical systems,to the problem of tracing the parameter de...
Convergence to Diffusion Waves for Nonlinear Evolution Equations with Ellipticity and Damping, and with Different End States
evolution equations diffusion waves decay rate energy method a priori estimates
2007/12/11
In this paper, we consider the global existence and the asymptotic behavior of solutions to the Cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects:...