圆锥区域中变系数半线性抛物型微分不等式的刘维尔型定理

研究圆锥区域中变系数半线性抛物型微分不等式及其耦合不等式组的刘维尔型定理.先给出弱解的定义,再利用构造试验函数法建立不依赖于初始值的解的universal估计,最后得到非负非平凡整体弱解的在适当的临界指数范围内不存在的结论,此种方法的主要特点是不用比较原理和极值原理.

Liouville Theorems of Semi-linear Parabolic DifferentialInequalities with Variable Coefficients in Cone

In this paper,the Liouville type theorems of semi-linear parabolic differential inequalities and systems of coupling inequalities with variable coefficients in cone were invertigated.First global weak solution was defined and the Universal estimation(independent of the initial value) of the solution was ertablished by constructing the test function,then the nonexistence of nonnegative non-trivial global weak solution within the appropriate critical exponent was achieved.The specialty of this method is that it does not use comparison theorems or the maximum principle.