A Note to the Cauchy Problem for the Degenerate Parabolic Equations with Strongly Nonlinear Sources (Journal of Partial Differential Equations, 2009)
In this note we study the nonexistence of nontrivial global solutions on S=R^N×(0,∞) for the following inequalities: |u|_t≥Δ(|u|^{m-1}u)+|u|^q, and  |u|_t≥div(|∇u|^{p-2}∇|u|)+|u|^q. When m, p, q satisfy some given conditions, the nonexistence of nontrivial global solution is proved, without taking their traces on the hyperplans t=0 into account.