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Article type: Research Article
Authors: Disconzi, Marcelo M.a; * | Shao, Yuanzhenb
Affiliations: [a] Vanderbilt University, Nashville, TN, USA | [b] The University of Alabama, Tuscaloosa, AL, USA
Correspondence: [*] Corresponding author. E-mail: [email protected].
Abstract: 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.
Keywords: Strong hyperbolicity, first-order quasilinear systems, relativistic fluids
DOI: 10.3233/ASY-241919
Journal: Asymptotic Analysis, vol. 140, no. 3-4, pp. 281-302, 2024
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