Hyperbolic to Parabolic Relaxation Theory for Quasilinear First Order Systems
By Pierangelo Marcati, Bruno Rubino. 2000
104 citations recorded by the source corpus.
Abstract In this paper we study the limiting behavior of nonhomogeneous hyperbolic systems of balance laws when the relaxed equilibria are described by means of systems of parabolic type. In particular we obtain a complete theory for the 2×2 systems of genuinely nonlinear hyperbolic balance laws in 1≳D with a strong dissipative term. A different method, which combines the div–curl lemma with accretive operators, is then applied to study the limiting profiles in the case of nonhomogeneous isentropic gas dynamics. We also investigate relaxation results for some 2≳D cases, which include the Cattaneo model for nonlinear heat conduction and the compressible Euler flow. Moreover, convergence result is also obtained for general semilinear systems in 1≳D.
Subfields: Applied Mathematics, Computational Mechanics, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/6d4351d6878adefa7a6c17c791b0ae7326896f95
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In Applied Mathematics
In Computational Mechanics
In Control and Systems Engineering
Citations in the corpus
- L1 Convergence to the Barenblatt Solution for Compressible Euler Equations with Damping (2011, background): “In the case away from vacuum, system (1.1) can be transferred to the damped p-system by changing to the Lagrangian coordinates; see [ 32 ,43].”
- Asymptotic behavior of the solutions to the damped compressible Euler equations with vacuum (2006, background): “Another interesting paper related to the same issue of [26] is [27], where the singular limit problems are discussed for hyperbolic relaxation to parabolic equations.”