Moscow Mathematical Journal

Volume 16, Issue 2, April–June 2016 pp. 299–321.

Separable Differential Operators and Applications

Authors: Veli B. Shakhmurov (1)
Author institution:(1) Department of Mechanical Engineering, Okan University, Akfirat, Tuzla 34959 Istanbul, Turkey; and Department of Mathematics, Azerbaycan Khazar University

Summary:

The nonlocal boundary value problems for degenerate differential-operator equations with variable coefficients are studied. The Lp separability properties of elliptic problems and well-posedeness of parabolic problems in mixed Lp spaces are derived. Then by using the regularity properties of linear problems, the existence and uniqueness of solution of nonlinear elliptic problem is obtained. Note that applications of these problems can be models of different physics process.

2010 Math. Subj. Class. 35xx, 35Kxx, 47Hxx, 34Bxx, 43Axx, 46Bxx.

Keywords: Abstract harmonic analysis, differential-operator equations, degenerate PDE, semigroups of operators, Sobolev–Lions spaces, separable differential operators.

Contents Full-Text PDF