Weak well-posedness for the two-component <italic style="font-style: italic">b</italic> family system

WU Tiantian; LIU Jingjing

doi:10.13471/j.cnki.acta.snus.2019.11.22.2019A087

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Weak well-posedness for the two-component b family system

Research articles | 更新时间：2023-11-01

- Weak well-posedness for the two-component b family system
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 59, Issue 6, Pages: 154-162(2020)
- 作者机构：
  
  郑州轻工业大学数学与信息科学学院，河南郑州 450002
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2019.11.22.2019A087
  CLC： O175
- Published：25 November 2020，
  
  Received：22 November 2019，
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吴甜甜,刘静静.两个分量的b族方程组的弱适定性[J].中山大学学报(自然科学版),2020,59(06):154-162.

WU Tiantian,LIU Jingjing.Weak well-posedness for the two-component b family system[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2020,59(06):154-162.
吴甜甜,刘静静.两个分量的b族方程组的弱适定性[J].中山大学学报(自然科学版),2020,59(06):154-162. DOI： 10.13471/j.cnki.acta.snus.2019.11.22.2019A087.

WU Tiantian,LIU Jingjing.Weak well-posedness for the two-component b family system[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2020,59(06):154-162. DOI： 10.13471/j.cnki.acta.snus.2019.11.22.2019A087.

摘要

使用特征线方法得到了两个分量的

族方程组的Cauchy问题当初值

</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo stretchy="false">)</mo><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msup><mo stretchy="false">(</mo><mi mathvariant="normal">ℝ</mi><mo stretchy="false">)</mo><mo>⋂</mo><msup><mrow><mi>W</mi></mrow><mrow><mn mathvariant="normal">1</mn><mo>

</mo><mi mathvariant="normal">∞</mi></mrow></msup><mo stretchy="false">(</mo><mi mathvariant="normal">ℝ</mi><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo stretchy="false">(</mo><mi mathvariant="normal">ℝ</mi><mo stretchy="false">)</mo><mo>⋂</mo><msup><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">∞</mi></mrow></msup><mo stretchy="false">(</mo><mi mathvariant="normal">ℝ</mi><mo stretchy="false">)</mo></math>

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49490338&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49490337&type=

60.28266525

4.31799984

时解的弱适定性。首先，将两个分量的

族方程组转化为一个ODE系统，其次通过解的存在唯一性理论，得到该ODE系统解的存在唯一性，最后由该ODE系统与两个分量的

族方程组之间的关系，得到两个分量的

族方程组解的存在唯一性并给出解关于初值稳定性的结论。

Abstract

By using the characteristic line method， the weak well-posedness of the Cauchy problem of the two-component

family system is obtained when the initial value

</mo><mi mathvariant="normal">∞</mi></mrow></msup><mo stretchy="false">(</mo><mi mathvariant="normal">ℝ</mi><mo stretchy="false">)</mo></math>

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49490340&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49490339&type=

41.74066544

5.07999992

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49490342&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49490341&type=

25.56933403

3.97933340

. Firstly， the

family system is transformed into an ODE system. Then， the existence and uniqueness of the solution of the ODE system are obtained by the existence and uniqueness theory of the solution. Finally， the existence and uniqueness of the solution of the

family system are obtained by the relationship between the two-component

family system and the ODE system. Moreover， the stability of the solutions with respect to the initial value is given.

关键词

两个分量的b族方程组弱适定性特征线方法

Keywords

two-component b family systemweak well-posednesscharacteristic line method

references

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GUAN C， ZHU H. Well-posedness of a class of solutions to an integrable two-component Camassa–Holm system ［J］. Journal of Mathematical Analysis and Applications，2018.

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LINARES F， PONCE G， SIDERIS T C. Properties of solutions to the Camassa-Holm equation on the line in a class containing the peakons ［J］. arXiv，2016.［arXiv:1609.06212]

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Weak well-posedness for a Degasperis-Procesi equation

Related Author

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Related Institution

Department of Mathematics, South China Agricultural University

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⁰

Weak well-posedness for the two-component b family system

DOI：10.13471/j.cnki.acta.snus.2019.11.22.2019A087

摘要

Abstract

关键词

Keywords

references