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fujita phenomena in nonlinear pseudo-parabolic system

Science China Mathematics 2014年第3期57卷 555-568页

作者： YANG JinGe CAO Yang ZHENG SiNing School of Mathematical Sciences Dalian University of Technology

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.

关键词： semilinear pseudo-parabolic system critical fujita exponent second critical exponent global profile

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critical exponents for Fast Diffusion Equations with Nonlinear Boundary Sources

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Communications in Mathematical Research 2011年第2期27卷 97-104页

作者： WANG LU-SHENG WANG ZE-JIA School of Mathematics Jilin University Changehun 130012

In this paper,we study the large time behavior of solutions to a class of fast diffusion equations with nonlinear boundary sources on the exterior domain of the unit *** are interested in the critical global exponent q_o and the critical fujita exponent q_c for the problem considered,and show that q_o=q_c for the multidimensional Non-Newtonian polytropic filtration equation with nonlinear boundary sources,which is quite different from the known results that q_o〈q_c for the onedimensional case;moreover,the value is different from the slow case.

关键词： exterior domain critical global exponent critical fujita exponent fast diffusion equation

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