Asymptotic analysis of some boundary value problems with singular perturbations. (Q2778954)

The authors of this monograph investigate some classes of hyperbolic partial differential systems with nonlinear boundary conditions, which contain small parameters. These singularly perturbed problems represent mathematical models for various applications in electrotechnics and mechanics. Zero or first-order asymptotic expansions with respect to the small parameter for the solutions of the problems are obtained. Using the method of \textit{M. I. Vishik} and \textit{L. A. Lyusternik} [Transl. (2), Am. Math. Soc. 20, 239-364 (1962; Zbl 0122.32402); translation from Usp. Mat. Nauk 12, No. 5, 3-122 (1957; Zbl 0087.29602)], it is proved that the solutions of the considered systems, called perturbed, corrected by the so-called boundary layer functions, approximate in different topologies the solutions of the systems obtained by neglecting the small parameters, called unperturbed.NEWLINENEWLINENEWLINEAlso, in the same context, some singularly perturbed coupled problems of elliptic or parabolic type, considered in two subdomains of a given domain, with transmission conditions at the interface, are studied.NEWLINENEWLINENEWLINEThe monograph contains the results obtained by the authors during the last years in the field of the asymptotic analysis and it is the first Romanian book on this subject, devoted to the partial differential equations.