1,231 research outputs found
A threshold phenomenon for embeddings of into Orlicz spaces
We consider a sequence of positive smooth critical points of the
Adams-Moser-Trudinger embedding of into Orlicz spaces. We study its
concentration-compactness behavior and show that if the sequence is not
precompact, then the liminf of the -norms of the functions is greater
than or equal to a positive geometric constant.Comment: 14 Page
Periodic solutions for completely resonant nonlinear wave equations
We consider the nonlinear string equation with Dirichlet boundary conditions
, with odd and analytic,
, and we construct small amplitude periodic solutions with frequency
\o for a large Lebesgue measure set of \o close to 1. This extends previous
results where only a zero-measure set of frequencies could be treated (the ones
for which no small divisors appear). The proof is based on combining the
Lyapunov-Schmidt decomposition, which leads to two separate sets of equations
dealing with the resonant and nonresonant Fourier components, respectively the
Q and the P equations, with resummation techniques of divergent powers series,
allowing us to control the small divisors problem. The main difficulty with
respect the nonlinear wave equations , ,
is that not only the P equation but also the Q equation is infinite-dimensiona
The regularized 3D Boussinesq equations with fractional Laplacian and no diffusion
In this paper, we study the 3D regularized Boussinesq equations. The velocity
equation is regularized \`a la Leray through a smoothing kernel of order
in the nonlinear term and a -fractional Laplacian; we consider
the critical case and we assume . The temperature equation is a pure transport equation, where
the transport velocity is regularized through the same smoothing kernel of
order . We prove global well posedness when the initial velocity is in
and the initial temperature is in for
. This regularity is enough to prove uniqueness of
solutions. We also prove a continuous dependence of the solutions on the
initial conditions.Comment: 28 pages; final version accepted for publication in Journal of
Differential Equation
Brain drain and development traps
This paper links the two fields of 'development traps' and 'brain drain'. We construct a model which integrates endogenous international migration into a simple growth model. As a result the dynamics of the economy can feature some underdevelopment traps: an economy starting with a low level of human capital can be caught in a vicious circle where low level of human capital leads to low wages, and low wages leads to emigration of valuable human capital. We also show that our model displays a rich array of different dynamic regimes, including the above traps, but other regimes as well, and we link explicitly the nature of the regimes to technology and policy parameters
Existence and Uniqueness of Solutions to Nonlinear Evolution Equations with Locally Monotone Operators
In this paper we establish the existence and uniqueness of solutions for
nonlinear evolution equations on Banach space with locally monotone operators,
which is a generalization of the classical result by J.L. Lions for monotone
operators. In particular, we show that local monotonicity implies the
pseudo-monotonicity. The main result is applied to various types of PDE such as
reaction-diffusion equations, generalized Burgers equation, Navier-Stokes
equation, 3D Leray- model and -Laplace equation with non-monotone
perturbations.Comment: 29 page
Numerical Approximation using Evolution PDE Variational Splines
This article deals with a numerical approximation method using an evolutionary partial differential equation
(PDE) by discrete variational splines in a finite element space. To formulate the problem, we need an evolutionary
PDE equation with respect to the time and the position, certain boundary conditions and a set of
approximating points. We show the existence and uniqueness of the solution and we study a computational
method to compute such a solution. Moreover, we established a convergence result with respect to the time
and the position. We provided several numerical and graphic examples of approximation in order to show
the validity and effectiveness of the presented method
Data-adaptive harmonic spectra and multilayer Stuart-Landau models
Harmonic decompositions of multivariate time series are considered for which
we adopt an integral operator approach with periodic semigroup kernels.
Spectral decomposition theorems are derived that cover the important cases of
two-time statistics drawn from a mixing invariant measure.
The corresponding eigenvalues can be grouped per Fourier frequency, and are
actually given, at each frequency, as the singular values of a cross-spectral
matrix depending on the data. These eigenvalues obey furthermore a variational
principle that allows us to define naturally a multidimensional power spectrum.
The eigenmodes, as far as they are concerned, exhibit a data-adaptive character
manifested in their phase which allows us in turn to define a multidimensional
phase spectrum.
The resulting data-adaptive harmonic (DAH) modes allow for reducing the
data-driven modeling effort to elemental models stacked per frequency, only
coupled at different frequencies by the same noise realization. In particular,
the DAH decomposition extracts time-dependent coefficients stacked by Fourier
frequency which can be efficiently modeled---provided the decay of temporal
correlations is sufficiently well-resolved---within a class of multilayer
stochastic models (MSMs) tailored here on stochastic Stuart-Landau oscillators.
Applications to the Lorenz 96 model and to a stochastic heat equation driven
by a space-time white noise, are considered. In both cases, the DAH
decomposition allows for an extraction of spatio-temporal modes revealing key
features of the dynamics in the embedded phase space. The multilayer
Stuart-Landau models (MSLMs) are shown to successfully model the typical
patterns of the corresponding time-evolving fields, as well as their statistics
of occurrence.Comment: 26 pages, double columns; 15 figure
A Dissipative Model for Hydrogen Storage: Existence and Regularity Results
We prove global existence of a solution to an initial and boundary value
problem for a highly nonlinear PDE system. The problem arises from a
thermomechanical dissipative model describing hydrogen storage by use of metal
hydrides. In order to treat the model from an analytical point of view, we
formulate it as a phase transition phenomenon thanks to the introduction of a
suitable phase variable. Continuum mechanics laws lead to an evolutionary
problem involving three state variables: the temperature, the phase parameter
and the pressure. The problem thus consists of three coupled partial
differential equations combined with initial and boundary conditions. Existence
and regularity of the solutions are here investigated by means of a time
discretization-a priori estimates-passage to the limit procedure joined with
compactness and monotonicity arguments
Existence of maximizers for Sobolev-Strichartz inequalities
We prove the existence of maximizers of Sobolev-Strichartz estimates for a
general class of propagators, involving relevant examples, as for instance the
wave, Dirac and the hyperbolic Schrodinger flows.Comment: 10 page
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