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1.
We obtain results of existence and multiplicity of solutions for the second-order equation x″+q(t)g(x)=0, with x(t) defined for all t∈]0,1[ and such that x(t)→+∞ as t→0+ and t→1−. We assume g having superlinear growth at infinity and q(t) possibly changing sign on [0,1]. 相似文献
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3.
Local bifurcation control is a topic of fundamental importance in the field of nonlinear dynamical systems. We discuss an original example within the context of storage-ring free-electron laser physics by presenting a new model that enables analytical insight into the system dynamics. The transition between the stable and the unstable regimes, depending on the temporal overlapping between the light stored in the optical cavity and the electrons circulating into the ring, is found to be a Hopf bifurcation. A feedback procedure is implemented and shown to provide an effective stabilization of the unstable steady state. 相似文献
4.
Pata Vittorino; Zheng Ken Xiaojun; Zucchi Adele 《Journal London Mathematical Society》2000,61(2):604-616
Every subalgebra of L(H) which is isometrically weak*-homeomorphicwith H() is reflexive, when is a finitely connected regionin the complex plane. 相似文献
5.
In this paper we find a relation between the lattice of hyperinvariant subspaces of an operatorT of classC
0 over a multiply connected region and that of its Jordan modelT. It is shown that, generally, the lattice corresponding toT can be identified with a retract of that corresponding toT. Thus the Jordan model has the smallest lattice of hyperinvariant subspaces in a given quasisimilarity class. 相似文献
6.
We consider the singular limit of the semilinear strongly damped wave equation with memory in the presence of a critical nonlinearity,
as the memory kernel converges to the Dirac mass at zero. We prove the existence of a robust family of regular exponential
attractors in the weak energy space.
Partially supported by the Italian PRIN research project 2006 Problemi a frontiera libera, transizioni di fase e modelli di isteresi. The first author has been partially supported by a research grant from the Fondazione Fratelli Confalonieri (Milano, Italy). 相似文献
7.
A weakly damped wave equation in the three‐dimensional (3‐D) space with a damping coefficient depending on the displacement is studied. This equation is shown to generate a dissipative semigroup in the energy phase space, which possesses finite‐dimensional global and exponential attractors in a slightly weaker topology. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
8.
H.G. Rotstein et al. proposed a nonconserved phase-field system characterized by the presence of memory terms both in the heat conduction and
in the order parameter dynamics. These hereditary effects are represented by time convolution integrals whose relaxation kernels
k and h are nonnegative, smooth and decreasing. Rescaling k and h properly, we obtain a system of coupled partial integrodifferential equations depending on two relaxation times ɛ and σ.
When ɛ and σ tend to 0, the formal limiting system is the well-known nonconserved phase-field model proposed by G. Caginalp.
Assuming the exponential decay of the relaxation kernels, the rescaled system, endowed with homogeneous Neumann boundary conditions,
generates a dissipative strongly continuous semigroup Sɛ, σ(t) on a suitable phase space, which accounts for the past histories of the temperature as well as of the order parameter. Our
main result consists in proving the existence of a family of exponential attractors
for Sɛ, σ(t), with ɛ, σ ∈ [0, 1], whose symmetric Hausdorff distance from
tends to 0 in an explicitly controlled way. 相似文献
9.
Vittorino Pata Ramon Quintanilla 《Journal of Mathematical Analysis and Applications》2010,363(1):19-3605
The decay of solutions in nonsimple elasticity with memory is addressed, analyzing how the decay rate is influenced by the different dissipation mechanisms appearing in the equations. In particular, a first order dissipation is shown to guarantee the asymptotic stability of the related solution semigroup, but is not strong enough to entail exponential stability. The latter occurs for a dissipation mechanism of the second order, that is, the same order as the one of the leading operator. 相似文献
10.
Malbor?Asllani Tommaso?Biancalani Duccio?FanelliEmail author Alan J.?McKane 《The European Physical Journal B - Condensed Matter and Complex Systems》2013,86(11):476
Stochastic reaction-diffusion models can be analytically studied on complex networks using the linear noise approximation. This is illustrated through the use of a specific stochastic model, which displays travelling waves in its deterministic limit. The role of stochastic fluctuations is investigated and shown to drive the emergence of stochastic waves beyond the region of the instability predicted from the deterministic theory. Simulations are performed to test the theoretical results and are analyzed via a generalized Fourier transform algorithm. This transform is defined using the eigenvectors of the discrete Laplacian defined on the network. A peak in the numerical power spectrum of the fluctuations is observed in quantitative agreement with the theoretical predictions. 相似文献