Maksimov, A. M.; Radkevich, E. V. Nonsimultaneous resonances in porous media. (English. Russian original) Zbl 0827.35104 Differ. Equations 29, No. 12, 1878-1887 (1993); translation from Differ. Uravn. 29, No. 12, 2149-2159 (1993). A mathematical model is considered for a three-dimensional two- temperature porous medium filled by a viscous liquid partly being in the form of a film. The dynamic process of propagation of nonlinear waves in such a deformable medium is described by the Cauchy problem for a system of partial differential equations. In order to determine conditions for the existence of resonance modes the authors carry out an asymptotic analysis based on Maslov’s nonlinear WKB-method and the technique of multiscale expansions. For this purpose the original model is transformed to nonlinear evolution equations describing the propagation of the high- frequency elastic waves as well as the low-frequency filtrational and thermal ones. The main theorem proves the existence of an asymptotic solution for the reduced system. In conclusion the essential influence of dispersion and nonlinearities is shown in generating modulated waves. Reviewer: V.Chernyatin (Szczecin) Cited in 1 Document MSC: 35Q35 PDEs in connection with fluid mechanics 35Q53 KdV equations (Korteweg-de Vries equations) 76S05 Flows in porous media; filtration; seepage 35G25 Initial value problems for nonlinear higher-order PDEs 81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory Keywords:Cauchy problem; propagation of nonlinear waves; existence of resonance modes; Maslov’s nonlinear WKB-method; technique of multiscale expansions; influence of dispersion and nonlinearities PDFBibTeX XMLCite \textit{A. M. Maksimov} and \textit{E. V. Radkevich}, Differ. Equations 29, No. 12, 1 (1993; Zbl 0827.35104); translation from Differ. Uravn. 29, No. 12, 2149--2159 (1993)