A numerical study of high-pressure droplet vaporization

We investigate a boundary-functional problem with transmission conditions for ordinary differential-operator equation in Sobolev spaces with a weight. We prove an isomorphism, coerciveness with respect to the spectral parameter, completeness and Abel basis of a system of root functions of the problem. Obtained results in the article are new even in case of Sobolev spaces without the weight.

Problems for Ordinary Differential Equations with Transmission Conditions

Modelling of thermochemical plumes and implications for the origin of the Siberian traps

Thermal-moisture analogy schemes for a moisture diffusion analysis are reviewed. Two schemes for practical applications are described using the governing equations of heat and mass diffusions: (1) direct analogy and (2) normalized analogy. The schemes are implemented to define valid domains of application. The results corroborate that the direct analogy is valid only for single-material systems, but the normalized analogy can be extended to multimaterial systems if thermal loading conditions are isothermal, spatially as well as temporally.

On Moisture Diffusion Modeling Using Thermal-Moisture Analogy

In this paper, we deal with Sturm–Liouville-type problems when the potential of the differential equation may have discontinuity at one inner point and the eigenparameter appears not only in the differential equation, but also in both boundary and transmission conditions. By modifying some techniques of (Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions. Proc. R. Soc. Edin. 1977; 77A:293–308; Eigenfunction Expenses Associated with Second-Order Differential Equations I (2nd edn). Oxford University Press: London, 1962) we generalize some results of the classic regular Sturm–Liouville problems. In particular, we construct Green's function, and derive asymptotic approximation formulae for Green's function. Further, we introduce a new operator-theoretic formulation in suitable Hilbert space such a way that the considered problem can be interpreted as the eigenvalue problem of this operator and constract the resolvent of this operator in terms of Green's function. Finally, we estimate the norm of resolvent of this operator. Copyright © 2007 John Wiley & Sons, Ltd.

Yu.A. Mikhailov

Papers

Theory of heat and mass transfer.