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ASYMPTOTIC STABILITY OF ASCENDING SOLITARY MAGMA WAVES
Journal article   Open access   Peer reviewed

ASYMPTOTIC STABILITY OF ASCENDING SOLITARY MAGMA WAVES

Gideon Simpson and Michael I. Weinstein
SIAM journal on mathematical analysis, v 40(4), pp 1337-1391
01 Jan 2008
DOI: https://doi.org/10.1137/080712271
Featured in Collection :   UN Sustainable Development Goals @ Drexel
url
http://arxiv.org/abs/0801.0463View
Submitted Open Open Access (License Unspecified)

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
Coherent structures, such as solitary waves, appear in many physical problems, including fluid mechanics, optics, quantum physics, and plasma physics. A less studied setting is found in geophysics, where highly viscous fluids couple to evolving material parameters, modeling partially molten rock, magma, in the Earth's interior. Solitary waves are also found here, but the equations lack useful mathematical structures such as an inverse scattering transform or even a variational formulation. A common question in all of these applications is whether or not these structures are stable to perturbation. We prove that the solitary waves in this earth science setting are asymptotically stable and accomplish this without any preexisting Lyapunov stability. This holds true for a family of equations, extending beyond the physical parameter space. Furthermore, this extends existing results on well-posedness to data in a neighborhood of the solitary waves.

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11 Record Views
15 citations in Web of Science
14 citations in Scopus

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Web of Science research areas
Mathematics, Applied
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