328 research outputs found
Dimension Estimate for the Global Attractor of an Evolution Equation
No full textWe estimate the dimension of the global attractor of an evolution equation by the study of the evolution of the n-dimensional volumes under the flow. We compare these results with the estimate of the dimension of the inertial manifold
Hyperbolic Relaxation of a Fourth Order Evolution Equation
No full textWe propose a hyperbolic relaxation of a fourth order evolution equation,
with an inertial term , where . We prove the existence of several absorbing sets having different regularities and the existence of a global attractor that is bounded in
Asymptotic behavior of a fourth order evolution equation
No full textWe study the asymptotic behavior of a singularly perturbed fourth order evolution equation related to the regularization of an ill posed equation encountering forward and backward diffusion. In particular we prove the existence of an exponential attractor and give an estimate of its dimension
On the stability analysis of a delayed two-stage Cournot model with R&D spillovers
No full textWe investigate the dynamics of Cournot's duopoly model with time delays, where firms compete at the R&D level and settle on their quantity based on shared earnings at the second stage. Stability conditions of the equilibrium points and occurrence of Hopf bifurcations are analyzed. Furthermore, we present numerical simulations to furnish experimented evidence for the system's complex behaviors
Dynamics of a Gross-Pitaevskii Equation with Phenomenological Damping
No full textWe study the dynamical behavior of solutions of an n-dimensional nonlinear Schrödinger equation with potential and linear derivative terms under the presence of phenomenological damping. This equation is a general version of the dissipative Gross-Pitaevskii equation including terms with first-order derivatives in the spatial coordinates which allow for rotational contributions. We obtain conditions for the existence of a global attractor and find bounds for its dimension
Periodic travelling waves for a fourth order nonlinear evolution equation
No full textIn this article we provide a travelling wave analysis for a fourth order non linear evolution equation. In particular we prove the existence of periodic travelling waves while we exclude the existence of solitary waves for proper values of the parameters. Moreover, we analyse the set of stationary solutions and provide a new proof of the existence of limit cycle for a related equation, that is, the Van der Pol equation
Recurrence analysis on Julia sets of semigroups of complex polynomials
No full textWe introduce a recurrence function in order to analyze the dynamics of semigroups of complex polynomials. We show that under a regularity hypothesis, the recurrence function is continuous in the complex plane. This is a new notion even for the case of a semigroup with just one generator
Density of backward paths on the Julia set of a semigroup.
No full textA well-known result from the theory of dynamics of semigroups
of rational functions is that the backward orbit of almost every
complex number accumulates on the Julia set of the semigroup. In this
article we significantly improve that result by giving a tree structure to
the backward orbit and showing that almost every path of the tree is
dense in the Julia set of the semigroup
An estimate concerning the difference between minimizer and boundary value in some polyconvex problems
No full textThis paper is concerned with regularity of minimizers of integral functionals with
polyconvex potentials. In particular we obtain
bounds on the difference for minimizers of
problem
%
egin{equation*}
minleft{
int_Omega f(x,Dv(x))dx,quad vin u_* + W_0^{1,p}(Omega,R^3)
ight}.
end{equation*
Precipitation–temperature changes and evolution of a small glacier in the southeastern European Alps during the last 90 years.
No full textVery small glaciers (area <0.1 km2) have received increased scientific attention during recent years, both for
their rapid responses to the climate forcing and because they are characterized by microclimatic conditions, often marginal to
glacier formation. They are particularly sensitive to climate changes and characterized by a great mass turnover, particularly
evident in maritime areas with high precipitation. Here we consider the evolution from 1920 of the ‘Canin Eastern Glacier’
(Italian Southeastern Alps) in order to correlate its evolution to the precipitation–temperature trends. We reconstructed a
precipitation–temperature record at the altitude of the glacier, filling a lack of knowledge in this alpine sector. We observed
a decrease in the mean annual precipitation of 10% in 90 years and a warming trend of 0.1∘C decade−1 since 1851, and of
0.7∘C decade−1 in the last 20 years. An inverse correlation between precipitation and mean air temperature during summer and
ablation periods was also observed. Glacier dynamics revealed a phase of stability between 1945 and 1985 that seems to be
a peculiar characteristic of this area. Moreover, through a general regression model the glacial terminus variations seem to be
statistically influenced only by winter precipitation. This fact opens interesting perspectives for the possible future evolution
of this small glacier and, more in general, to other small glaciers in maritime areas in regard to climate change scenarios
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