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Research Article | Open Access

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

Giuseppe Maria Coclite1( ), Lorenzo di Ruvo2
Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, via E. Orabona 4, 70125 Bari, Italy
Dipartimento di Matematica, Università di Bari, via E. Orabona 4, 70125 Bari, Italy
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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.

Keywords

existenceuniquenessstabilityKuramoto-Velarde equationinitial-boundary value problem

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Networks and Heterogeneous Media
Volume 21 Issue 1,
March 2026
Pages 92-146
DOI: 10.3934/nhm.2026005

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Coclite GM, di Ruvo L. On the initial-boundary value problem for a Kuramoto-Velarde equation. Networks and Heterogeneous Media, 2026, 21(1): 92-146. https://doi.org/10.3934/nhm.2026005

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Received: 09 July 2025
Revised: 30 December 2025
Accepted: 05 January 2026
Published: 15 March 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)