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A Note to the Cauchy Problem for the Degenerate Parabolic Equations with Strongly Nonlinear Sources
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@Article{JPDE-22-199,
author = {Tingting Zheng and Junning Zhao },
title = {A Note to the Cauchy Problem for the Degenerate Parabolic Equations with Strongly Nonlinear Sources},
journal = {Journal of Partial Differential Equations},
year = {2009},
volume = {22},
number = {3},
pages = {199--204},
abstract = {
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.
}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v22.n3.1}, url = {http://global-sci.org/intro/article_detail/jpde/5253.html} }
TY - JOUR
T1 - A Note to the Cauchy Problem for the Degenerate Parabolic Equations with Strongly Nonlinear Sources
AU - Tingting Zheng & Junning Zhao
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 -
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.
Tingting Zheng and Junning Zhao . (2009). A Note to the Cauchy Problem for the Degenerate Parabolic Equations with Strongly Nonlinear Sources.
Journal of Partial Differential Equations. 22 (3).
199-204.
doi:10.4208/jpde.v22.n3.1
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