On the initial-boundary value problem for a Kuramoto-Sinelshchikov type equation

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

doi:10.3934/mine.2021036

Mathematics in Engineering

2021, Volume 3, Issue 4: 1-43. doi: 10.3934/mine.2021036

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Research article

On the initial-boundary value problem for a Kuramoto-Sinelshchikov 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, Universita di Bari, via E. Orabona 4, 70125 Bari, Italy

Received: 28 July 2020 Accepted: 23 August 2020 Published: 08 September 2020

The Kuramoto-Sinelshchikov equation describes the evolution of a phase turbulence in reaction-diffusion systems or the evolution of the plane flame propagation, taking in account the combined influence of diffusion and thermal conduction of the gas on the stability of a plane flame front. In this paper, we prove the well-posedness of the classical solutions for the initial-boundary value problem for this equation, under appropriate boundary conditions.
- existence,
- uniqueness,
- stability,
- Kuramoto-Sinelshchikov type equation,
- initial-boundary value problem
Citation: Giuseppe Maria Coclite, Lorenzo di Ruvo. On the initial-boundary value problem for a Kuramoto-Sinelshchikov type equation[J]. Mathematics in Engineering, 2021, 3(4): 1-43. doi: 10.3934/mine.2021036

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Abstract

The Kuramoto-Sinelshchikov equation describes the evolution of a phase turbulence in reaction-diffusion systems or the evolution of the plane flame propagation, taking in account the combined influence of diffusion and thermal conduction of the gas on the stability of a plane flame front. In this paper, we prove the well-posedness of the classical solutions for the initial-boundary value problem for this equation, under appropriate boundary conditions.

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