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Results tagged with ap.analysis-of-pdes
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user 50614
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
1
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Are solutions of the Beltrami Equations necessarily smooth?
Let $ a $, $ b $ and $ c $ be real constants such that $ \Delta \stackrel{\text{df}}{=} a c - b^{2} > 0 $. The Beltrami Equations are defined as the following system of PDE’s on the domain $ \Bbb{R}^{ …
- 1,396
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0
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On the differentiability of a certain map from $ (0,\infty) $ to $ \Bbb{R} $
This problem arose from my study of energy-conservation for non-linear Schrödinger equations. Suppose that we have the following data:
$ u \in C^{1} \! \left( (0,\infty),{L^{2}}(\Bbb{R}^{n}) \right) …
- 1,396
9
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Some Mathematical Questions on Gravitational Waves and Numerical Relativity
Due to the recent spate of detections of gravitational waves by LIGO, my amateurish interest in the mathematics of general relativity has been revived.
The wave-forms of the detected gravitational wa …
- 1,396