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We introduce a new approach to the study of modulation of high-frequency periodic wave patterns, based on pseudodifferential analysis, multi-scale expansion, and Kreiss symmetrizer estimates like those in hyperbolic and hyperbolic-parabolic boundary-value theory. Key ingredients are local Floquet transformation as a preconditioner removing large derivatives in the normal direction of background rapidly oscillating fronts and the use of the periodic Evans function of Gardner to connect spectral information on component periodic waves to block structure of the resulting approximately constant-coefficient resolvent ODEs. Our main result is bounded-time existence and validity to all orders of large-amplitude smooth modulations of planar periodic solutions of multi-D reaction diffusion systems in the high-frequency/small wavelength limit.
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This content will become publicly available on November 4, 2025
Strongly hyperbolic quasilinear systems revisited, with applications to relativistic fluid dynamics
We revisit the theory of first-order quasilinear systems with diagonalizable principal part and only real eigenvalues, what is commonly referred to as strongly hyperbolic systems. We provide a self-contained and simple proof of local well-posedness, in the Hadamard sense, of the Cauchy problem. Our regularity assumptions are very minimal. As an application, we apply our results to systems of ideal and viscous relativistic fluids, where the theory of strongly hyperbolic equations has been systematically used to study several systems of physical interest.
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- PAR ID:
- 10591157
- Publisher / Repository:
- IOS Press
- Date Published:
- Journal Name:
- Asymptotic Analysis
- Volume:
- 140
- Issue:
- 3-4
- ISSN:
- 0921-7134
- Page Range / eLocation ID:
- 281 to 302
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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