On the Global Stability of Solutions of Moment Systems in Nonequilibrium Thermodynamics |
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Authors: | Radkevich E V |
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Institution: | (1) M. V. Lomonosov Moscow State University, Russia |
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Abstract: | In this paper, we study the linearization of the Cauchy problem and the mixed problem for the system of Grad--Hermite moments in nonequilibrium thermodynamics in the neighborhood of the equilibrium state. Stability conditions for solutions of the Cauchy problem are proved as a generalization of the classical Hermite--Biller theorem on stable polynomials. For the mixed problem, we prove an analog of the Vishik--Lyusternik theorem on small singular perturbations of general elliptic problems. The last observation allows us to introduce the Shapiro--Lopatinskii condition, which implies the well-posedness of the mixed problem. |
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Keywords: | Grad--Hermite moment problem conservation laws with relaxation linearization stability condition polynomial bundles Cauchy problem Shapiro--Lopatinskii condition |
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