Volume 30, Issue 2
Blow-up Sets to a Coupled Heat System

Jinhuan Wang & Liang Hong

Commun. Math. Res., 30 (2014), pp. 117-130.

Published online: 2021-05

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  • Abstract

This paper deals with a heat system coupled via local and localized sources subject to null Dirichlet boundary conditions. In a previous paper of the authors, a complete result on the multiple blow-up rates was obtained. In the present paper, we continue to consider the blow-up sets to the system via a complete classification for the nonlinear parameters. That is the discussion on single point versus total blow-up of the solutions. It is mentioned that due to the influence of the localized sources, there is some substantial difficulty to be overcomed there to deal with the single point blow-up of the solutions.

  • Keywords

coupled localized source, coupled local source, total blow-up, single point blow-up, blow-up set.

  • AMS Subject Headings

35K55, 35B33

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-30-117, author = {Wang , Jinhuan and Hong , Liang}, title = {Blow-up Sets to a Coupled Heat System}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {30}, number = {2}, pages = {117--130}, abstract = {

This paper deals with a heat system coupled via local and localized sources subject to null Dirichlet boundary conditions. In a previous paper of the authors, a complete result on the multiple blow-up rates was obtained. In the present paper, we continue to consider the blow-up sets to the system via a complete classification for the nonlinear parameters. That is the discussion on single point versus total blow-up of the solutions. It is mentioned that due to the influence of the localized sources, there is some substantial difficulty to be overcomed there to deal with the single point blow-up of the solutions.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2014.02.03}, url = {http://global-sci.org/intro/article_detail/cmr/18974.html} }
TY - JOUR T1 - Blow-up Sets to a Coupled Heat System AU - Wang , Jinhuan AU - Hong , Liang JO - Communications in Mathematical Research VL - 2 SP - 117 EP - 130 PY - 2021 DA - 2021/05 SN - 30 DO - http://doi.org/10.13447/j.1674-5647.2014.02.03 UR - https://global-sci.org/intro/article_detail/cmr/18974.html KW - coupled localized source, coupled local source, total blow-up, single point blow-up, blow-up set. AB -

This paper deals with a heat system coupled via local and localized sources subject to null Dirichlet boundary conditions. In a previous paper of the authors, a complete result on the multiple blow-up rates was obtained. In the present paper, we continue to consider the blow-up sets to the system via a complete classification for the nonlinear parameters. That is the discussion on single point versus total blow-up of the solutions. It is mentioned that due to the influence of the localized sources, there is some substantial difficulty to be overcomed there to deal with the single point blow-up of the solutions.

Jinhuan Wang & Liang Hong. (2021). Blow-up Sets to a Coupled Heat System. Communications in Mathematical Research . 30 (2). 117-130. doi:10.13447/j.1674-5647.2014.02.03
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