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Second critical exponent for a higher-order semilinear parabolic system 被引量:1
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作者 YANG ChunXiao YANG JinGe ZHENG SiNing 《Science China Mathematics》 SCIE CSCD 2015年第7期1453-1460,共8页
This paper studies a higher-order semilinear parabolic system. We obtain the second critical exponent to characterize the critical space-decay rate of the initial data in the co-existence parameter region of global an... This paper studies a higher-order semilinear parabolic system. We obtain the second critical exponent to characterize the critical space-decay rate of the initial data in the co-existence parameter region of global and non-global solutions. Together with the critical Fujita exponent established by Pang et al.(2006),this gives a clear and complete picture to the Fujita phenomena in the coupled higher-order semilinear parabolic system. 展开更多
关键词 higher-order semilinear parabolic system second critical exponent global existence BLOW-UP
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Fujita phenomena in nonlinear pseudo-parabolic system 被引量:6
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作者 YANG JinGe CAO Yang ZHENG SiNing 《Science China Mathematics》 SCIE 2014年第3期555-568,共14页
This paper deals with the Cauchy problem to the nonlinear pseudo-parabolic system ut - △u - αut =vp, vt -△v - α△vt = uq with p, q≥ 1 and pq 〉 1, where the viscous terms of third order are included. We first fin... This paper deals with the Cauchy problem to the nonlinear pseudo-parabolic system ut - △u - αut =vp, vt -△v - α△vt = uq with p, q≥ 1 and pq 〉 1, where the viscous terms of third order are included. We first find the critical Fujita exponent, and then determine the second critical exponent to characterize the critical space-decay rate of initial data in the co-existence region of global and non-global solutions. Moreover, time-decay profiles are obtained for the global solutions. It can be found that, different from those for the situations of general semilinear heat systems, we have to use distinctive techniques to treat the influence from the viscous terms of the highest order. To fix the non-global solutions, we exploit the test function method, instead of the general Kaplan method for heat systems. To obtain the global solutions, we apply the LP-Lq technique to establish some uniform Lm time-decay estimates. In particular, under a suitable classification for the nonlinear parameters and the initial data, various Lm time-decay estimates in the procedure enable us to arrive at the time-decay profiles of solutions to the system. It is mentioned that the general scaling method for parabolic problems relies heavily on regularizing effect to establish the compactness of approximating solutions, which cannot be directly realized here due to absence of the smooth effect in the pseudo-parabolic system. 展开更多
关键词 semilinear pseudo-parabolic system critical Fujita exponent second critical exponent global profile
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