$ H^1 $ solutions for a modified Korteweg-de Vries-Burgers type equation

Giuseppe Maria Coclite; Lorenzo di Ruvo; Giuseppe Maria Coclite; Lorenzo di Ruvo

doi:10.3934/nhm.2024032

Networks and Heterogeneous Media

2024, Volume 19, Issue 2: 724-739. doi: 10.3934/nhm.2024032

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$ H^1 $ solutions for a modified Korteweg-de Vries-Burgers type equation

Giuseppe Maria Coclite ^{1
,
,},
Lorenzo di Ruvo ²

1.
Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, via E. Orabona 4, 70125 Bari, Italy
2.
Dipartimento di Matematica, Università di Bari, via E. Orabona 4, 70125 Bari, Italy

Received: 13 February 2024 Revised: 24 June 2024 Accepted: 08 July 2024 Published: 15 July 2024

This paper modeled the dynamics of microbubbles coated with viscoelastic shells using the modified Korteweg-de Vries-Burgers equation, a nonlinear third-order partial differential equation. This study focused on the well-posedness of the Cauchy problem associated with this equation.
- existence,
- uniqueness,
- stability,
- a modified Korteweg-de Vries-Burgers type equation,
- cauchy problem
Citation: Giuseppe Maria Coclite, Lorenzo di Ruvo. $ H^1 $ solutions for a modified Korteweg-de Vries-Burgers type equation[J]. Networks and Heterogeneous Media, 2024, 19(2): 724-739. doi: 10.3934/nhm.2024032

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Abstract

This paper modeled the dynamics of microbubbles coated with viscoelastic shells using the modified Korteweg-de Vries-Burgers equation, a nonlinear third-order partial differential equation. This study focused on the well-posedness of the Cauchy problem associated with this equation.

References

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