Files and links (2)
SubmittedOpen Access (License Unspecified), Open
Journal article
On a Hamiltonian PDE arising in magma dynamics
Discrete and continuous dynamical systems. Series B, v 10(4), pp 903-924
01 Nov 2008
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
In this article we discuss a new Hamiltonian PDE arising from a class of equations appearing in the study of magma, partially molten rock in the Earth's interior. Under physically justifiable simplifications, a scalar, non-linear, degenerate, dispersive wave equation may be derived to describe the evolution of phi, the fraction of molten rock by volume, in the Earth. These equations have two power nonlinearities which specify the constitutive realitions for bulk viscosity and permeability in terms of phi. Previously, they have been shown to admit solitary wave equation to be Hamiltonian; it can be viewed as a generalization of the Benjamin-Bona-Mahoney equation. We prove that the solitary waves are nonlinearly stable, by showing that they are constrained local minimizers of an appropriate time-invariant Lyapunov functional. A consequence is an extension of the regime of global in time well-posedness for this class of equations to (large) data which includes a neighborhood of a solitary traveling waves with compact spatial support.
Metrics
Details
- Title
- On a Hamiltonian PDE arising in magma dynamics
- Creators
- Gideon Simpson - Columbia Univ, Dept Appl Phys & Appl Math, New York, NY 10027 USAMichael I. Weinstein - Columbia Univ, Dept Appl Phys & Appl Math, New York, NY 10027 USAPhilip Rosenau - Tel Aviv Univ, Sch Math Sci, IL-69978 Tel Aviv, IsraelDepartment of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027
- Publication Details
- Discrete and continuous dynamical systems. Series B, v 10(4), pp 903-924
- Publisher
- Amer Inst Mathematical Sciences-Aims
- Number of pages
- 22
- Grant note
- 558/99-2 / Israeli Science Foundation; Israel Science Foundation DGE-0221041 / NSF Integrative Graduate Education and Research Traineeship (IGERT); National Science Foundation (NSF) DMS-0530853 / Division of Mathematical Sciences (DMS); National Science Foundation (NSF); NSF - Directorate for Mathematical & Physical Sciences (MPS) US National Science Foundation (NSF) Collaboration in Mathematical Geosciences (CMG); National Science Foundation (NSF) DMS-0412305; DMS-0707850 / NSF; National Science Foundation (NSF) 0530853 / Direct For Mathematical & Physical Scien; National Science Foundation (NSF); NSF - Directorate for Mathematical & Physical Sciences (MPS)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000259354800010
- Scopus ID
- 2-s2.0-57749169697
- Other Identifier
- 991019296814304721
UN Sustainable Development Goals (SDGs)
This publication has contributed to the advancement of the following goals:
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics, Applied