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Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation. (English) Zbl 0587.35046
A connection between the strict dissipativity of a partial differential equations system and the decay of its solutions is fixed. The decay property is used to prove the existence of in t global solutions of nonlinear evolution equations provided the initial data are sufficient small. As examples global solvability for Navier-Stokes equations and for some models of kinetic theory is proved.
Reviewer: N.A.Lar’kin

35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35Q30 Navier-Stokes equations
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