Modern methods of partial differential equations for engineering - Rakhimov, Abdumalik A. (2013)

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In the paper we examine some problems for partial differential equations of engineering using the concepts of the theory of distributions. The paper is devoted to specify the modern methods of Partial Differential Equation (PDE) for engineering. Here we discus recently developed methods of the spectral theory of the partial differential equations in the spaces of distributions. In particular convergence and summability problems of the spectral expansions associated with the selfadjoint extensions of the elliptic partial differential operator studied in the spaces of distributions. In this we prove sharp conditions of localization and summability of the expansions of the distributions.