9,906 research outputs found
Adaptive ℋ∞-control for nonlinear systems: a dissipation theoretical approach
The adaptive ℋ∞-control problem for parameter-dependent nonlinear systems with full information feedback is considered. The techniques from dissipation theory as well as the vector and parameter projection methods are used to derive the adaptive ℋ∞-control laws. Both of the projection techniques are rigorously treated. The adaptive robust stabilization for nonlinear systems with ℒ2-gain hounded uncertainties is investigated
Global well-posedness and scattering of the (4+1)-dimensional Maxwell-Klein-Gordon equation
This article constitutes the final and main part of a three-paper sequence,
whose goal is to prove global well-posedness and scattering of the energy
critical Maxwell-Klein-Gordon equation (MKG) on for
arbitrary finite energy initial data. Using the successively stronger
continuation/scattering criteria established in the previous two papers, we
carry out a blow-up analysis and deduce that the failure of global
well-posedness and scattering implies the existence of a nontrivial stationary
or self-similar solution to MKG. Then, by establishing that such solutions do
not exist, we complete the proof.Comment: 64 page
Nonconcentration of energy for a semilinear Skyrme model
We continue our investigation of a model introduced by Adkins and Nappi, in
which omega mesons stabilize chiral solitons. The aim of this article is to
show that the energy associated to equivariant solutions does not concentrate.Comment: 12 pages, 2 figure
A vector field method for relativistic transport equations with applications
We adapt the vector field method of Klainerman to the study of relativistic
transport equations. First, we prove robust decay estimates for velocity
averages of solutions to the relativistic massive and massless transport
equations, without any compact support requirements (in or ) for the
distribution functions. In the second part of this article, we apply our method
to the study of the massive and massless Vlasov-Nordstr\"om systems. In the
massive case, we prove global existence and (almost) optimal decay estimates
for solutions in dimensions under some smallness assumptions. In the
massless case, the system decouples and we prove optimal decay estimates for
the solutions in dimensions for arbitrarily large data, and in
dimension under some smallness assumptions, exploiting a certain form of
the null condition satisfied by the equations. The -dimensional massive case
requires an extension of our method and will be treated in future work.Comment: 72 pages, 3 figure
Decay of the Maxwell field on the Schwarzschild manifold
We study solutions of the decoupled Maxwell equations in the exterior region
of a Schwarzschild black hole. In stationary regions, where the Schwarzschild
coordinate ranges over , we obtain a decay rate of
for all components of the Maxwell field. We use vector field methods
and do not require a spherical harmonic decomposition.
In outgoing regions, where the Regge-Wheeler tortoise coordinate is large,
, we obtain decay for the null components with rates of
, , and . Along the event horizon and in ingoing regions, where ,
and when , all components (normalized with respect to an ingoing null
basis) decay at a rate of C \uout^{-1} with \uout=t+r_* in the exterior
region.Comment: 37 pages, 5 figure
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