Stability of quasi-linear hyperbolic dissipative systems
Heinz Otto Kreiss (1), Omar E. Ortiz (2), Oscar A. Reula (2) ((1), Department of Mathematics, UCLA, USA, (2) FaMAF, Universidad Nacional de, Cordoba, Argentina)
TL;DR
This paper investigates how eigenvalue conditions of first-order PDE operators relate to the stability of their stationary solutions, enhancing understanding of stability criteria in hyperbolic dissipative systems.
Contribution
It establishes a connection between eigenvalue conditions and stability, providing new insights into the stability analysis of quasi-linear hyperbolic dissipative systems.
Findings
Eigenvalue conditions influence stability criteria
Linear stability is characterized by specific eigenvalue properties
Nonlinear stability results are derived from eigenvalue analysis
Abstract
In this work we want to explore the relationship between certain eigenvalue condition for the symbols of first order partial differential operators describing evolution processes and the linear and nonlinear stability of their stationary solutions.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Aquatic and Environmental Studies · Differential Equations and Boundary Problems