Dan, Wakako On a local in time solvability of the Neumann problem of quasilinear hyperbolic parabolic coupled systems. (English) Zbl 0841.35003 Math. Methods Appl. Sci. 18, No. 13, 1053-1082 (1995). The author prvoes a local (in time) existence theorem of classical solutions to some coupled systems of quasilinear hyperbolic equations and quasilinear parabolic equations with Neumann boundary conditions which are fully nonlinear. An iteration scheme, extending that used by Y. Shibata and M. Kikuchi [J. Differ. Equations 80, 154-197 (1989; Zbl 0689.35055)] for a hyperbolic system, leads to the solution by successive approximation through appropriate linearization and the study of hyperbolic-parabolic-elliptic systems. The equations of nonlinear thermoelasticity are a typical example. Reviewer: R.Racke (Konstanz) Cited in 2 Documents MSC: 35A07 Local existence and uniqueness theorems (PDE) (MSC2000) Keywords:quasilinear hyperbolic parabolic coupled systems; Neumann boundary conditions; successive approximation; nonlinear thermoelasticity Citations:Zbl 0689.35055 PDFBibTeX XMLCite \textit{W. Dan}, Math. Methods Appl. Sci. 18, No. 13, 1053--1082 (1995; Zbl 0841.35003) Full Text: DOI References: [1] Chrz??szczyk, Arch. Mech. 39 pp 605– (1987) [2] Chrz??szczyk, Tsukuba J. Math. 16 pp 443– (1992) [3] Dan, Tsukuba J. Math 18 pp 411– (1994) [4] Jiang, Math. Meth. in the Appl. Sci. 12 pp 315– (1990) [5] ’Systems of a hyperbolic-parabolic composite type, with applications to the equations of magnetohydrodynamics’, Thesis, Kyoto University (1983). [6] Mukoyama, Tsukuba J. Math. 13 pp 363– (1989) [7] Lectures on Nonlinear Evolution Equations: Initial Value Problems, Aspects of mathematics: E; Vol. 19, Friedr. Vieweg & Sohn, Braunschweig/Wiesbaden, 1992. · doi:10.1007/978-3-663-10629-6 [8] Shibata, Funkcial. Ekvac. 25 pp 303– (1982) [9] ’On a local existence theorem for some quasilinear hyperbolic-parabolic coupled systems with Neumann type boundary condition’, Manuscript, 1989. [10] Shibata, J. Diff. Eqns. 80 pp 154– (1989) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.