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Volume 22, Issue 3
A Note to the Cauchy Problem for the Degenerate Parabolic Equations with Strongly Nonlinear Sources

Tingting Zheng & Junning Zhao

DOI: 10.4208/jpde.v22.n3.1

J. Part. Diff. Eq., 22 (2009), pp. 199-204.

Published online: 2009-08

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  • 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.

  • Keywords

Nonlinear sources global solutions nonexistence

  • AMS Subject Headings

35K65 35K55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-22-199, author = {}, 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 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 & Junning Zhao . (2019). 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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