Blow-up of solutions for a time fractional biharmonic equation with exponentional nonlinear memory
In the paper, we focus on the local existence and blow-up of solutions for a time fractional nonlinear equation with biharmonic operator and exponentional nonlinear memory in an Orlicz space. We first establish a $ L^p-L^q $ estimate for solution operators of a time fractional nonlinear biharmonic e...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-11-01
|
| Series: | Electronic Research Archive |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024278 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590732039290880 |
|---|---|
| author | Yuchen Zhu |
| author_facet | Yuchen Zhu |
| author_sort | Yuchen Zhu |
| collection | DOAJ |
| description | In the paper, we focus on the local existence and blow-up of solutions for a time fractional nonlinear equation with biharmonic operator and exponentional nonlinear memory in an Orlicz space. We first establish a $ L^p-L^q $ estimate for solution operators of a time fractional nonlinear biharmonic equation, and obtain bilinear estimates for mild solutions. Then, based on the contraction mapping principle, we establish the local existence of mild solutions. Moreover, by using the test function method, we obtain the blow-up result of solutions. |
| format | Article |
| id | doaj-art-2cf8ccf53aaa43a88e41937db89793ed |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-2cf8ccf53aaa43a88e41937db89793ed2025-01-23T07:53:00ZengAIMS PressElectronic Research Archive2688-15942024-11-0132115988600710.3934/era.2024278Blow-up of solutions for a time fractional biharmonic equation with exponentional nonlinear memoryYuchen Zhu0College of Mathematics & Statistics, Nanjing University of Information Science & Technology, Nanjing 210044, ChinaIn the paper, we focus on the local existence and blow-up of solutions for a time fractional nonlinear equation with biharmonic operator and exponentional nonlinear memory in an Orlicz space. We first establish a $ L^p-L^q $ estimate for solution operators of a time fractional nonlinear biharmonic equation, and obtain bilinear estimates for mild solutions. Then, based on the contraction mapping principle, we establish the local existence of mild solutions. Moreover, by using the test function method, we obtain the blow-up result of solutions.https://www.aimspress.com/article/doi/10.3934/era.2024278fractional biharmonic equationexponentional nonlinear memoryblow-uplocal existence |
| spellingShingle | Yuchen Zhu Blow-up of solutions for a time fractional biharmonic equation with exponentional nonlinear memory Electronic Research Archive fractional biharmonic equation exponentional nonlinear memory blow-up local existence |
| title | Blow-up of solutions for a time fractional biharmonic equation with exponentional nonlinear memory |
| title_full | Blow-up of solutions for a time fractional biharmonic equation with exponentional nonlinear memory |
| title_fullStr | Blow-up of solutions for a time fractional biharmonic equation with exponentional nonlinear memory |
| title_full_unstemmed | Blow-up of solutions for a time fractional biharmonic equation with exponentional nonlinear memory |
| title_short | Blow-up of solutions for a time fractional biharmonic equation with exponentional nonlinear memory |
| title_sort | blow up of solutions for a time fractional biharmonic equation with exponentional nonlinear memory |
| topic | fractional biharmonic equation exponentional nonlinear memory blow-up local existence |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024278 |
| work_keys_str_mv | AT yuchenzhu blowupofsolutionsforatimefractionalbiharmonicequationwithexponentionalnonlinearmemory |