Blow-up of solutions for nonlinear wave equations on locally finite graphs
Let $ G = (V, E) $ be a local finite connected weighted graph, $ \Omega $ be a finite subset of $ V $ satisfying $ \Omega^\circ\neq\emptyset $. In this paper, we study the nonexistence of the nonlinear wave equation $ \partial^2_t u = \Delta u + f(u) $ on $ G $. Under the appropriate conditi...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-05-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023922?viewType=HTML |
| _version_ | 1797806353944674304 |
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| author | Desheng Hong |
| author_facet | Desheng Hong |
| author_sort | Desheng Hong |
| collection | DOAJ |
| description | Let $ G = (V, E) $ be a local finite connected weighted graph, $ \Omega $ be a finite subset of $ V $ satisfying $ \Omega^\circ\neq\emptyset $. In this paper, we study the nonexistence of the nonlinear wave equation
$ \partial^2_t u = \Delta u + f(u) $
on $ G $. Under the appropriate conditions of initial values and nonlinear term, we prove that the solution for nonlinear wave equation blows up in a finite time. Furthermore, a numerical simulation is given to verify our results. |
| first_indexed | 2024-03-13T06:06:05Z |
| format | Article |
| id | doaj.art-26860184ec994142a8d35358fe93bf84 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-13T06:06:05Z |
| publishDate | 2023-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-26860184ec994142a8d35358fe93bf842023-06-12T01:20:57ZengAIMS PressAIMS Mathematics2473-69882023-05-0188181631817310.3934/math.2023922Blow-up of solutions for nonlinear wave equations on locally finite graphsDesheng Hong0School of Mathematics, Renmin University of China, Beijing 100872, ChinaLet $ G = (V, E) $ be a local finite connected weighted graph, $ \Omega $ be a finite subset of $ V $ satisfying $ \Omega^\circ\neq\emptyset $. In this paper, we study the nonexistence of the nonlinear wave equation $ \partial^2_t u = \Delta u + f(u) $ on $ G $. Under the appropriate conditions of initial values and nonlinear term, we prove that the solution for nonlinear wave equation blows up in a finite time. Furthermore, a numerical simulation is given to verify our results.https://www.aimspress.com/article/doi/10.3934/math.2023922?viewType=HTMLnonlinear wave equationblow uplocally finite graph |
| spellingShingle | Desheng Hong Blow-up of solutions for nonlinear wave equations on locally finite graphs AIMS Mathematics nonlinear wave equation blow up locally finite graph |
| title | Blow-up of solutions for nonlinear wave equations on locally finite graphs |
| title_full | Blow-up of solutions for nonlinear wave equations on locally finite graphs |
| title_fullStr | Blow-up of solutions for nonlinear wave equations on locally finite graphs |
| title_full_unstemmed | Blow-up of solutions for nonlinear wave equations on locally finite graphs |
| title_short | Blow-up of solutions for nonlinear wave equations on locally finite graphs |
| title_sort | blow up of solutions for nonlinear wave equations on locally finite graphs |
| topic | nonlinear wave equation blow up locally finite graph |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023922?viewType=HTML |
| work_keys_str_mv | AT deshenghong blowupofsolutionsfornonlinearwaveequationsonlocallyfinitegraphs |