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Volume 38, Issue 4
Blow-Up Phenomena for Some Pseudo-Parabolic Equations with Nonlocal Term

Gongwei Liu & Shuying Tian

DOI: 10.4208/ata.OA-2019-0021

Anal. Theory Appl., 38 (2022), pp. 451-466.

Published online: 2023-01

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  • Abstract

We investigate the initial boundary value problem of some semilinear pseudo-parabolic equations with Newtonian nonlocal term. We establish a lower bound for the blow-up time if blow-up does occur. Also both the upper bound for $T$ and blow up rate of the solution are given when $J(u_0)<0$. Moreover, we establish the blow up result for arbitrary initial energy and the upper bound for $T$. As a product, we refine the lifespan when $J(u_0)<0.$

  • Keywords

Nonlocal pseudo-parabolic equations, blow-up, upper bound, lower bound.

  • AMS Subject Headings

35B44, 35K70

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{ATA-38-451, author = {Liu , Gongwei and Tian , Shuying}, title = {Blow-Up Phenomena for Some Pseudo-Parabolic Equations with Nonlocal Term}, journal = {Analysis in Theory and Applications}, year = {2023}, volume = {38}, number = {4}, pages = {451--466}, abstract = {

We investigate the initial boundary value problem of some semilinear pseudo-parabolic equations with Newtonian nonlocal term. We establish a lower bound for the blow-up time if blow-up does occur. Also both the upper bound for $T$ and blow up rate of the solution are given when $J(u_0)<0$. Moreover, we establish the blow up result for arbitrary initial energy and the upper bound for $T$. As a product, we refine the lifespan when $J(u_0)<0.$

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2019-0021}, url = {http://global-sci.org/intro/article_detail/ata/21359.html} }
TY - JOUR T1 - Blow-Up Phenomena for Some Pseudo-Parabolic Equations with Nonlocal Term AU - Liu , Gongwei AU - Tian , Shuying JO - Analysis in Theory and Applications VL - 4 SP - 451 EP - 466 PY - 2023 DA - 2023/01 SN - 38 DO - http://doi.org/10.4208/ata.OA-2019-0021 UR - https://global-sci.org/intro/article_detail/ata/21359.html KW - Nonlocal pseudo-parabolic equations, blow-up, upper bound, lower bound. AB -

We investigate the initial boundary value problem of some semilinear pseudo-parabolic equations with Newtonian nonlocal term. We establish a lower bound for the blow-up time if blow-up does occur. Also both the upper bound for $T$ and blow up rate of the solution are given when $J(u_0)<0$. Moreover, we establish the blow up result for arbitrary initial energy and the upper bound for $T$. As a product, we refine the lifespan when $J(u_0)<0.$

Gongwei Liu & Shuying Tian. (2023). Blow-Up Phenomena for Some Pseudo-Parabolic Equations with Nonlocal Term. Analysis in Theory and Applications. 38 (4). 451-466. doi:10.4208/ata.OA-2019-0021
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