Several Nonlinear Liouville Theorems In Parabolic Differential Inequalities

In this paper, we investigate global existence and nonexistence of solution for several typesnonlinear parabolic differential inequalities by making use of modified test function method.The main results can be summarized as follows:Firstly, We consider strongly p-coercive parabolic differential inequality with a gradient termand singular coefficients, and obtain nonlinear Liouville theorem of solution based on themodified test function method.Secondly. We consider Cauchy problem of strongly p-coercive parabolic differentialinequality with weighted nonlocal source term, and obtain nonexistence of nonnegativenontrivial global weak solutions based on the method of test function and some applicationexamples will be presented.Finally. We consider the initial boundary value problem of singular parabolic equations, andobtain the Fujita critical exponentq=(N-α)(m=1)/N-2based on the test function method andthe comparison principle.