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http://dx.doi.org/10.12941/jksiam.2011.15.1.043

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)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.15, no.1, 2011 , pp. 43-55 More about this Journal
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.
Keywords
slow diffusion parabolic differential inequalities; test function; Liouville theorem;
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