# LIOUVILLE THEOREMS OF SLOW DIFFUSION DIFFERENTIAL INEQUALITIES WITH VARIABLE COEFFICIENTS IN CONE

• Fang, Zhong Bo (SCHOOL OF MATHEMATICAL SCIENCES, OCEAN UNIVERSITY OF CHINA) ;
• Fu, Chao (SCHOOL OF MATHEMATICAL SCIENCES, OCEAN UNIVERSITY OF CHINA) ;
• Zhang, Linjie (SCHOOL OF MATHEMATICAL SCIENCES, OCEAN UNIVERSITY OF CHINA)
• Accepted : 2011.03.18
• Published : 2011.03.25

#### Abstract

We here investigate the Liouville type theorems of slow diffusion differential inequality and its coupled system with variable coefficients in cone. First, we give the definition of global weak solution, and then we establish the universal estimate (does not depend on the initial value) of solution by constructing test function. At last, we obtain the nonexistence of non-negative non-trivial global weak solution within the appropriate critical exponent. The main feature of this method is that we need not use comparison theorem or the maximum principle.

#### Acknowledgement

Supported by : Central Universities, NSFC

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