A Liouville-type theorem for a system of parabolic inequalities and its applications

作者：Xiang, Zhaoyin^*; Mu, Chunlai; Du, Lili

来源：Applied Mathematics Letters, 2007, 20(9): 976-981.

DOI：10.1016/j.aml.2006.10.002

• Liouville theorem
• a priori estimate
• inequalities
• Fujita phenomena

In this work, we study a system of parabolic inequalities. Using the method of test functions, we establish an integral estimate and get a Liouville-type theorem for the solutions of this system. As an application, we observe the well-known Fujita blow-up phenomena for the corresponding parabolic system. Here, the importance of this observation is that we do not impose any regularity assumption on the initial data. For general exponents, we also establish the universal LP estimates and obtain the nonexistence of solutions bounded below by a positive constant.

• 出版日期2007-9
• 单位华南理工大学; 中山大学; 四川大学; 电子科技大学