On the solutions for a Benney-Lin type equation

Giuseppe Maria Coclite; Lorenzo di Ruvo

doi:10.3934/dcdsb.2022024

Article Contents

2022, Volume 27, Issue 11: 6865-6883. Doi: 10.3934/dcdsb.2022024

This issue Previous Article Stochastic persistence in degenerate stochastic Lotka-Volterra food chains Next Article Stability and Hopf bifurcation in a prey-predator model with memory-based diffusion

On the solutions for a Benney-Lin type equation

Giuseppe Maria Coclite^1, , and
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

^*Corresponding author: Giuseppe Maria Coclite
^*Corresponding author: Giuseppe Maria Coclite

Received: May 2021

Revised: December 2021

Early access: February 2022

Published: November 2022

GMC is member of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). GMC has been partially supported by the Research Project of National Relevance "Multiscale Innovative Materials and Structures" granted by the Italian Ministry of Education, University and Research (MIUR Prin 2017, project code 2017J4EAYB and the Italian Ministry of Education, University and Research under the Programme Department of Excellence Legge 232/2016 (Grant No. CUP - D94I18000260001).

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Abstract

The Benney-Lin equation describes the evolution of long waves in various problems in fluid dynamics. In this paper, we prove the well-posedness of the Cauchy problem, associated with this equation.

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Mathematics Subject Classification: Primary: 35G25; Secondary: 35K55.

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