Global Existence And Blow-up Of Solutions Of Several Type Of Parabolic Equations

In this paper, we investigate several types of nonlinear parabolic equations, and establishexistence and nonexistence results of global solutions and blow up properties. The mainresults can be summarized as follows:Chapter1. Study initial boundary value problems of nonlinear parabolic equations andobtain existence results of blow-up solutions with positive initial energy by using modifiedconvexity method.Chapter2. Investigate initial boundary value problems of quasi-linear parabolic equationswith gradient terms, provide sufficient conditions for the existence of global and blow-upsolutions, the upper bounds for the "blow-up time", the "upper estimates" of the "blow-up rate"and the "upper estimates" of the global solution by constructing auxiliary functions and usingmaximum principal and upper-low solution argument. Finally, some examples are presented asthe application of the obtained results.Chapter3. Consider Cauchy problem of quasi-linear parabolic inequalities with singularvariable coefficients in some functional space with parameters, and establish nonexistence resultof nonnegative nontrivial global weak solution in some appropriate range of critical exponentby constructing test function.Research of these problems has high scientific significance in improving and expandingnonlinear method and blow-up theory of parabolic equation and Liouville theorem.