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Dissipative structure for symmetric hyperbolic-parabolic systems with Korteweg-type dispersion. (English) Zbl 1484.35157

Summary: In this paper, we are concerned with generally symmetric hyperbolic-parabolic systems with Korteweg-type dispersion. Referring to those classical efforts by Kawashima et al., we formulate new structural conditions for the Korteweg-type dispersion and develop the dissipative mechanism of “regularity-gain type.” As an application, it is checked that several concrete model systems (e.g., the compressible Navier-Stokes(-Fourier)-Korteweg system) satisfy the general structural conditions. In addition, the optimality of our general theory on the dissipative structure is also verified by calculating the asymptotic expansions of eigenvalues.

MSC:

35G50 Systems of nonlinear higher-order PDEs
35B40 Asymptotic behavior of solutions to PDEs
35Q35 PDEs in connection with fluid mechanics
35Q53 KdV equations (Korteweg-de Vries equations)
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