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Journal article
Existence theory for magma equations in dimension two and higher
Nonlinearity, v 31(10), pp 4724-4745
01 Oct 2018
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Abstract
We examine a degenerate, dispersive, nonlinear wave equation related to the evolution of partially molten rock in dimensions two and higher. This simplified model, for a scalar field capturing the melt fraction by volume, has been studied by direct numerical simulation where it has been observed to develop stable solitary waves. In this work, we prove local in time well-posedness results for the time dependent equation, on both the whole space and the torus, for dimensions two and higher. We also prove the existence of the solitary wave solutions in dimensions two and higher.
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Details
- Title
- Existence theory for magma equations in dimension two and higher
- Creators
- David M. Ambrose - Drexel University, MathematicsGideon Simpson - Drexel UniversityJ. Douglas Wright - Drexel UniversityDennis G. Yang - Drexel University
- Publication Details
- Nonlinearity, v 31(10), pp 4724-4745
- Publisher
- Iop Publishing Ltd
- Number of pages
- 22
- Grant note
- DMS-1515849; DMS-1409018; DMS-1511488 / National Science Foundation; National Science Foundation (NSF) 1409018 / Division Of Mathematical Sciences; 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:000444190100003
- Scopus ID
- 2-s2.0-85054683260
- Other Identifier
- 991019169419904721
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- Web of Science research areas
- Mathematics, Applied
- Physics, Mathematical