The Initial-Finite Problems for Nonclassical Models of Mathematical Physics

S. A. Zagrebina

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 2, pp. 5-24

Résumé

The models of Mathematical Physics, whose representation in the form of equations or systems of partial differential equations do not fit one of the classical types such as elliptic, parabolic or hyperbolic, are called nonclassical. The article provides an overview of the author's results in the field of nonclassical models of Mathematical Physics for which the initial-finite problems, generalizing the Cauchy and Showalter, Sidorov conditions, are considered. Basic method for the research is the Sviridyuk relative spectrum theory. Abstract results are illustrated by the specific initial-finite problems for the equations and systems of equations in partial derivatives occurring in applications, namely, the theory of filtration, fluid dynamics and mesoscopic theory, considered on the sets of different geometrical structure.

Détail

Keywords: nonclassical models of Mathematical Physics, Plotnikov model, the Navier–Stokes system, the Barenblatt–Zheltov–Kochina equation, the (multipoint) initial-finite problems, the relative spectrum.

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