Abstract
In this paper we study the stability of homogeneous states in a continuous one spatial variable of conservation equations in Lagrangian coordinates, including terms of dissipation and relaxation. Local existence is proved applying Kawashima’s theorem for hyperbolic-parabolic systems [7]. We establish that when the subcharactertistic condition is satisfied, the structure of the system is not of regularity-loss type, but of the standard type, even though the linear term associated with relaxation is not symmetric nor positive semidefinite.
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Acknowledgements
This work was supported by a CONACYT grant A1-S-41007 “Bifurcaciones en el estudio de la existencia y estabilidad de soluciones de EDP”. We thank the unkown referees for their patience and valuable corrections and suggestions to improve the original version of this paper.
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Delgado, J., Saavedra, P. On the Decay of Solutions of the Linearized Equations of Conservation Equations with Viscosity and Relaxation. Qual. Theory Dyn. Syst. 21, 101 (2022). https://doi.org/10.1007/s12346-022-00630-w
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DOI: https://doi.org/10.1007/s12346-022-00630-w