This paper mainly deals with the higher-order coupled Kirchhoff-type equations with nonlinear strong damped and source terms in a bounded domain. We obtain some results that are estimation of the upper bounds of Hausd...This paper mainly deals with the higher-order coupled Kirchhoff-type equations with nonlinear strong damped and source terms in a bounded domain. We obtain some results that are estimation of the upper bounds of Hausdorff dimension and Fractal dimension of the global attractor.展开更多
It is proved that the global existence for the nonhomogeneous quasilinear wave equation with a localized weakly nonlinear dissipation in exterior domains.
The current lithospheric geodynamics and tectonophysics in the Baikal rift are discussed in terms of a nonlinear oscillator with dissipation.The nonlinear oscillator model is applicable to the area because stress chan...The current lithospheric geodynamics and tectonophysics in the Baikal rift are discussed in terms of a nonlinear oscillator with dissipation.The nonlinear oscillator model is applicable to the area because stress change shows up as quasi-periodic inharmonic oscillations at rifting attractor structures （RAS）.The model is consistent with the space-time patterns of regional seismicity in which coupled large earthquakes,proximal in time but distant in space,may be a response to bifurcations in nonlinear resonance hysteresis in a system of three oscillators corresponding to the rifting attractors.The space-time distribution of coupled MLH ＞ 5.5 events has been stable for the period of instrumental seismicity,with the largest events occurring in pairs,one shortly after another,on two ends of the rift system and with couples of smaller events in the central part of the rift.The event couples appear as peaks of earthquake ‘migration＇ rate with an approximately decadal periodicity.Thus the energy accumulated at RAS is released in coupled large events by the mechanism of nonlinear oscillators with dissipation.The new knowledge,with special focus on space-time rifting attractors and bifurcations in a system of nonlinear resonance hysteresis,may be of theoretical and practical value for earthquake prediction issues.Extrapolation of the results into the nearest future indicates the probability of such a bifurcation in the region,i.e.,there is growing risk of a pending M ≈ 7 coupled event to happen within a few years.展开更多
文摘This paper mainly deals with the higher-order coupled Kirchhoff-type equations with nonlinear strong damped and source terms in a bounded domain. We obtain some results that are estimation of the upper bounds of Hausdorff dimension and Fractal dimension of the global attractor.
文摘It is proved that the global existence for the nonhomogeneous quasilinear wave equation with a localized weakly nonlinear dissipation in exterior domains.
基金supported by grants 09-05-00014-a, and 08-05-90201-Mong_a from the Russian Foundation for Basic Research
文摘The current lithospheric geodynamics and tectonophysics in the Baikal rift are discussed in terms of a nonlinear oscillator with dissipation.The nonlinear oscillator model is applicable to the area because stress change shows up as quasi-periodic inharmonic oscillations at rifting attractor structures （RAS）.The model is consistent with the space-time patterns of regional seismicity in which coupled large earthquakes,proximal in time but distant in space,may be a response to bifurcations in nonlinear resonance hysteresis in a system of three oscillators corresponding to the rifting attractors.The space-time distribution of coupled MLH ＞ 5.5 events has been stable for the period of instrumental seismicity,with the largest events occurring in pairs,one shortly after another,on two ends of the rift system and with couples of smaller events in the central part of the rift.The event couples appear as peaks of earthquake ‘migration＇ rate with an approximately decadal periodicity.Thus the energy accumulated at RAS is released in coupled large events by the mechanism of nonlinear oscillators with dissipation.The new knowledge,with special focus on space-time rifting attractors and bifurcations in a system of nonlinear resonance hysteresis,may be of theoretical and practical value for earthquake prediction issues.Extrapolation of the results into the nearest future indicates the probability of such a bifurcation in the region,i.e.,there is growing risk of a pending M ≈ 7 coupled event to happen within a few years.
