Global existence and blow up of solutions for a class of coupled parabolic systems with logarithmic nonlinearity
According to the difference of the initial energy, we consider three cases about the global existence and blow-up of the solutions for a class of coupled parabolic systems with logarithmic nonlinearity. The three cases are the low initial energy, critical initial energy and high initial energy, resp...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-06-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2022398?viewType=HTML |
| _version_ | 1811344453422546944 |
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| author | Qigang Deng Fugeng Zeng Dongxiu Wang |
| author_facet | Qigang Deng Fugeng Zeng Dongxiu Wang |
| author_sort | Qigang Deng |
| collection | DOAJ |
| description | According to the difference of the initial energy, we consider three cases about the global existence and blow-up of the solutions for a class of coupled parabolic systems with logarithmic nonlinearity. The three cases are the low initial energy, critical initial energy and high initial energy, respectively. For the low initial energy and critical initial energy $ J(u_0, v_0)\leq d $, we prove the existence of global solutions with $ I(u_0, v_0)\geq 0 $ and blow up of solutions at finite time $ T < +\infty $ with $ I(u_0, v_0) < 0 $, where $ I $ is Nehari functional. On the other hand, we give sufficient conditions for global existence and blow up of solutions in the case of high initial energy $ J(u_0, v_0) > d $. |
| first_indexed | 2024-04-13T19:47:35Z |
| format | Article |
| id | doaj.art-d2f0fd2bec0848a693d2d974f5bc1ea1 |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-04-13T19:47:35Z |
| publishDate | 2022-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-d2f0fd2bec0848a693d2d974f5bc1ea12022-12-22T02:32:40ZengAIMS PressMathematical Biosciences and Engineering1551-00182022-06-011988580860010.3934/mbe.2022398Global existence and blow up of solutions for a class of coupled parabolic systems with logarithmic nonlinearityQigang Deng0Fugeng Zeng1Dongxiu Wang2School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, ChinaSchool of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, ChinaSchool of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, ChinaAccording to the difference of the initial energy, we consider three cases about the global existence and blow-up of the solutions for a class of coupled parabolic systems with logarithmic nonlinearity. The three cases are the low initial energy, critical initial energy and high initial energy, respectively. For the low initial energy and critical initial energy $ J(u_0, v_0)\leq d $, we prove the existence of global solutions with $ I(u_0, v_0)\geq 0 $ and blow up of solutions at finite time $ T < +\infty $ with $ I(u_0, v_0) < 0 $, where $ I $ is Nehari functional. On the other hand, we give sufficient conditions for global existence and blow up of solutions in the case of high initial energy $ J(u_0, v_0) > d $.https://www.aimspress.com/article/doi/10.3934/mbe.2022398?viewType=HTMLcoupled parabolic systemsglobal existenceblow uplogarithmic nonlinearity |
| spellingShingle | Qigang Deng Fugeng Zeng Dongxiu Wang Global existence and blow up of solutions for a class of coupled parabolic systems with logarithmic nonlinearity Mathematical Biosciences and Engineering coupled parabolic systems global existence blow up logarithmic nonlinearity |
| title | Global existence and blow up of solutions for a class of coupled parabolic systems with logarithmic nonlinearity |
| title_full | Global existence and blow up of solutions for a class of coupled parabolic systems with logarithmic nonlinearity |
| title_fullStr | Global existence and blow up of solutions for a class of coupled parabolic systems with logarithmic nonlinearity |
| title_full_unstemmed | Global existence and blow up of solutions for a class of coupled parabolic systems with logarithmic nonlinearity |
| title_short | Global existence and blow up of solutions for a class of coupled parabolic systems with logarithmic nonlinearity |
| title_sort | global existence and blow up of solutions for a class of coupled parabolic systems with logarithmic nonlinearity |
| topic | coupled parabolic systems global existence blow up logarithmic nonlinearity |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2022398?viewType=HTML |
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