Dissipative structure for symmetric hyperbolic-parabolic systems with Korteweg-type dispersion. Issue 2 (7th February 2022)

• Record Type: Journal Article
• Authors: Kawashima, Shuichi; Shibata, Yoshihiro; Xu, Jiang
• Is Part Of: Communications in partial differential equations. Volume 47:Issue 2(2022)
• Page Start: 378
• Page End: 400
• Publication Date: 2022-02-07
• Subjects: Decay property -- dissipative structure -- Euler-Fourier-Korteweg system -- hyperbolic-parabolic systems -- Korteweg-type dispersion -- Navier-Stokes-Fourier-Korteweg system; 35G35 -- 35Q35 -- 35B35 -- 35B40; Differential equations, Partial -- Periodicals; 515.353
• DOI: 10.1080/03605302.2021.1983596
• Languages: English
• ISSNs: 0360-5302

Abstract

Abstract: 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.