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Existence results for the Kudryashov–Sinelshchikov–Olver equation

Part of: Parabolic equations and systems General higher-order equations and systems

Published online by Cambridge University Press:  01 April 2020

Giuseppe Maria Coclite  and
Lorenzo di Ruvo
Giuseppe Maria Coclite
Affiliation:
Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, via E. Orabona 4, 70125Bari, Italy (giuseppemaria.coclite@poliba.it)
Lorenzo di Ruvo
Affiliation:
Dipartimento di Matematica, Università di Bari, via E. Orabona 4, 70125Bari, Italy (lorenzo.diruvo77@gmail.com)
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Abstract

The Kudryashov–Sinelshchikov–Olver equation describes pressure waves in liquids with gas bubbles taking into account heat transfer and viscosity. In this paper, we prove the existence of solutions of the Cauchy problem associated with this equation.

Keywords

ExistenceKudryashov–Sinelshchikov–Olver equationCauchy problem

MSC classification

Primary: 35G25: Initial value problems for nonlinear higher-order equations
Secondary: 35K55: Nonlinear parabolic equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 2 , April 2021 , pp. 425 - 450
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Copyright
The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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Footnotes

*

The authors are members of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

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