On the initial-boundary value problem for a Kuramoto-Velarde equation

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

doi:10.3934/nhm.2026005

Networks and Heterogeneous Media

2026, Volume 21, Issue 1: 92-146. doi: 10.3934/nhm.2026005

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Research article

On the initial-boundary value problem for a Kuramoto-Velarde 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: 09 July 2025 Revised: 30 December 2025 Accepted: 05 January 2026 Published: 20 January 2026

The Kuramoto-Velarde equation describes the spatio-temporal evolution of step morphology on crystal surfaces, as well as the dynamics of spinodal decomposition in phase-separating systems subjected to an external field. In this paper, we prove the well-posedness of the solutions for the initial-boundary value problem for this equation, under several possible boundary conditions.
- existence,
- uniqueness,
- stability,
- Kuramoto-Velarde equation,
- initial-boundary value problem
Citation: Giuseppe Maria Coclite, Lorenzo di Ruvo. On the initial-boundary value problem for a Kuramoto-Velarde equation[J]. Networks and Heterogeneous Media, 2026, 21(1): 92-146. doi: 10.3934/nhm.2026005

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Abstract

The Kuramoto-Velarde equation describes the spatio-temporal evolution of step morphology on crystal surfaces, as well as the dynamics of spinodal decomposition in phase-separating systems subjected to an external field. In this paper, we prove the well-posedness of the solutions for the initial-boundary value problem for this equation, under several possible boundary conditions.

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