In this paper, we study the initial value problem for generalized Boussineq equation with weak damping. The existence and time-decay rates of global solutions its derivatives are established all space dimensions d ≥ 1, provided that norm data is suitably small. negative Sobolev norms in low frequency shown to be preserved along time evolution enhance decay solutions. proof based on energy metho...

Weak decay rates under stellar density and temperature conditions holding at the rapid proton-capture process are studied in neutron-deficient medium-mass waiting-point nuclei extending from Ni up to Sn. Neighboring isotopes to these waiting-point nuclei are also included in the analysis. The nuclear structure part of the problem is described within a deformed Skyrme Hartree-Fock + BCS + quasip...

In this paper we study the stabilization of the wave equation on general 1-d networks. For that, we transfer known observability results in the context of control of conservative systems (see [14]) into a weighted observability estimate for the dissipative one. Then we use an interpolation inequality similar to the one proved in [7] to obtain the explicit decay estimate of the energy for smooth...

The origin of chaotic behaviour of a dynamical system in the sense of sensitive dependence on initial conditions is the action of a certain group. We are used to the importance of a group from the theory of relativity and in fact this group happens to be a subgroup of the Poincare group. Physical consequences like sensitive dependence on initial conditions or exponential decay of time correlati...

*Correspondence: [email protected] School of Mathematical Science, Anhui University, Hefei, 230601, P.R. China Abstract This paper is concerned with the improved L2 decay for solutions of a class of the third-grade non-Newtonian fluid flows in R3. By developing the classic Fourier splitting methods, we prove the non-uniform decay of solutions when u0 ∈ L2(R3) and improve algebraic decay rates o...

This work discusses the asymptotic behavior of a transmission problem on star-shaped networks of interconnected elastic and thermoelastic rods. Elastic rods are undamped, of conservative nature, while the thermoelastic ones are damped by thermal effects. We analyze the overall decay rate depending of the number of purely elastic components entering on the system and the irrationality properties...

The origin of chaotic behaviour of a dynamical system in the sense of sensitive dependence on initial conditions is the action of a certain group. We are used to the importance of a group from the theory of relativity and in fact this group happens to be a subgroup of the Poincare group. Physical consequences like sensitive dependence on initial conditions or exponential decay of time correlati...