In this paper we show the decay of solutions to the initial-boundary value problem for some nonlinear hyperbolic equation with a nonlinear dissipative term, by using a difference inequality.
In the natural song of the mottled cicada, the prelude and loud song of the prolonging and repctition songs consist separatcly of several pulses containing the three subpulscs (SP1-3). The principal frequencies (PFban...In the natural song of the mottled cicada, the prelude and loud song of the prolonging and repctition songs consist separatcly of several pulses containing the three subpulscs (SP1-3). The principal frequencies (PFband PFc) of the basic sound and carricr frcquency band are 338±20 Hz and 3617±87 Hz, respectively.The prelude or the prolonging song contains 22 pulses (P1-22),and their amplitude-modulation propertics gradually decay. The carrier-wave oscillations gradually lose symmetrics and overlap with basic waves of the SP1, and the SP2,3 are similar to sine waves. Moreover, a dominant tone of the song gradually changes from PFc into PFb. In the loud song of the prolonging song, the prelude and loud song of repetition songs, the amplitude-modulation propcrties are lost.The carrier-wave oscillations mainly overlap with basic waves of the SP2, and the amplitudes of the PFc arc 10 dB over lower than those of the PFb, and the songs are the PFb of basic sounds as a dominant tone. In view of the structure of the sounding membrane, the vibration frequencies of the three long ribs may be gradually changed from mass controlling to mechanical resistance controlling, and corresponding songs are gradually changed from the prolonging prelude with the PFc as a dominant tone to the loud song and repetition songs with the PFb as a dominant tone.展开更多
This work is concerned with the time-fractional doubly parabolic Keller-Segel system in R^(N)(N≥1),and we derive some refined results on the large time behavior of solutions which are presupposed to enjoy some unifor...This work is concerned with the time-fractional doubly parabolic Keller-Segel system in R^(N)(N≥1),and we derive some refined results on the large time behavior of solutions which are presupposed to enjoy some uniform boundedness properties.Moreover,the well-posedness and the asymptotic stability of solutions in Marcinkiewicz spaces are studied.The results are achieved by means of an appropriate estimation of the system nonlinearity in the course of an analysis based on Duhamel-type representation formulae and the Kato-Fujita framework which consists in constructing a fixed-point argument by using a suitable time-dependent space.展开更多
Instead of the L^p estimates,we study the modulation space estimates for the solution to the damped wave equation.Decay properties for both the linear and semilinear equations are obtained.The estimates in modulation ...Instead of the L^p estimates,we study the modulation space estimates for the solution to the damped wave equation.Decay properties for both the linear and semilinear equations are obtained.The estimates in modulation space differ in many aspects from those in L^p space.展开更多
文摘In this paper we show the decay of solutions to the initial-boundary value problem for some nonlinear hyperbolic equation with a nonlinear dissipative term, by using a difference inequality.
文摘In the natural song of the mottled cicada, the prelude and loud song of the prolonging and repctition songs consist separatcly of several pulses containing the three subpulscs (SP1-3). The principal frequencies (PFband PFc) of the basic sound and carricr frcquency band are 338±20 Hz and 3617±87 Hz, respectively.The prelude or the prolonging song contains 22 pulses (P1-22),and their amplitude-modulation propertics gradually decay. The carrier-wave oscillations gradually lose symmetrics and overlap with basic waves of the SP1, and the SP2,3 are similar to sine waves. Moreover, a dominant tone of the song gradually changes from PFc into PFb. In the loud song of the prolonging song, the prelude and loud song of repetition songs, the amplitude-modulation propcrties are lost.The carrier-wave oscillations mainly overlap with basic waves of the SP2, and the amplitudes of the PFc arc 10 dB over lower than those of the PFb, and the songs are the PFb of basic sounds as a dominant tone. In view of the structure of the sounding membrane, the vibration frequencies of the three long ribs may be gradually changed from mass controlling to mechanical resistance controlling, and corresponding songs are gradually changed from the prolonging prelude with the PFc as a dominant tone to the loud song and repetition songs with the PFb as a dominant tone.
基金supported by the National Research and Development Agency of Chile(ANID)-Chile under Fondecyt(Grant No.1181084)。
文摘This work is concerned with the time-fractional doubly parabolic Keller-Segel system in R^(N)(N≥1),and we derive some refined results on the large time behavior of solutions which are presupposed to enjoy some uniform boundedness properties.Moreover,the well-posedness and the asymptotic stability of solutions in Marcinkiewicz spaces are studied.The results are achieved by means of an appropriate estimation of the system nonlinearity in the course of an analysis based on Duhamel-type representation formulae and the Kato-Fujita framework which consists in constructing a fixed-point argument by using a suitable time-dependent space.
基金supported by National Natural Science Foundation of China(Grant Nos.11201103 and 11471288)supported by the China Scholarship Council
文摘Instead of the L^p estimates,we study the modulation space estimates for the solution to the damped wave equation.Decay properties for both the linear and semilinear equations are obtained.The estimates in modulation space differ in many aspects from those in L^p space.
