Non-existence of the nontrivial solution for a Sobolev type evolution inequality with nonlinear convolution term

SU Jiahui; LIU Dengming

doi:10.13471/j.cnki.acta.snus.ZR20240250

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Non-existence of the nontrivial solution for a Sobolev type evolution inequality with nonlinear convolution term

Research articles | 更新时间：2025-11-14

- Non-existence of the nontrivial solution for a Sobolev type evolution inequality with nonlinear convolution term
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 64, Issue 5, Pages: 146-153(2025)
- 作者机构：
  
  湖南科技大学数学与统计学院，湖南湘潭 411201
- 作者简介：
  
  [ "SU Jiahuisujiahui@mail.hnust.edu.cn" ]
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.ZR20240250
  CLC： O175.2
- Received：07 August 2024，
  
  Revised：2025-05-15，
  
  Accepted：15 May 2025，
  
  Published Online：25 July 2025，
  
  Published：25 September 2025
- 稿件说明：
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苏佳慧,刘灯明.具有非线性卷积项的Sobolev型演化不等式非平凡解的不存在性[J].中山大学学报(自然科学版)(中英文),2025,64(05):146-153.

SU Jiahui,LIU Dengming.Non-existence of the nontrivial solution for a Sobolev type evolution inequality with nonlinear convolution term[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(05):146-153.
苏佳慧,刘灯明.具有非线性卷积项的Sobolev型演化不等式非平凡解的不存在性[J].中山大学学报(自然科学版)(中英文),2025,64(05):146-153. DOI： 10.13471/j.cnki.acta.snus.ZR20240250.

SU Jiahui,LIU Dengming.Non-existence of the nontrivial solution for a Sobolev type evolution inequality with nonlinear convolution term[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(05):146-153. DOI： 10.13471/j.cnki.acta.snus.ZR20240250.

摘要

研究一类具非线性卷积项的Sobolev型演化不等式. 结合非线性容量证法及反证法，给出了非平凡解的不存在性结果.

Abstract

An evolution inequality of Sobolev type involving a nonlinear convolution term is considered. By using the nonlinear capacity method and the contradiction argument

the non-existence of the nontrivial local weak solution is proved.

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Keywords

references

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