TY - JOUR
T1 - A Note to the Cauchy Problem for the Degenerate Parabolic Equations with Strongly Nonlinear Sources
JO - Journal of Partial Differential Equations
VL - 3
SP - 199
EP - 204
PY - 2009
DA - 2009/08
SN - 22
DO - http://doi.org/10.4208/jpde.v22.n3.1
UR - https://global-sci.org/intro/article_detail/jpde/5253.html
KW - Nonlinear sources
KW - global solutions
KW - nonexistence
AB - <p>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 &nbsp;|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.</p>