On The Cauchy Problem For Degenerate Parabolic Equations With Strongly Nonlinear Sources

This article includes two parts. First we considerwith initial traces by using new norms (?)f(?)_h and _h. We mainly consider about existence of local and global nonnegative solutions and their behaviors, gradient estimates and so on.The second part, we use some special test functions to deal with the nonexistence of non-trivial global solutions on S = R~N×(0,∞) for the following inequalitiesandWhen m, p, q satisfy some given conditions, the nonexistence of non-trivial global solution is proved without taking their traces on the hyperplans t = 0 into account. We can also deal withby using similar methods.