Investigation of nonlocal in time problems for first-order evolution and Schrödinger type equations

Author: marika gachechiladze
Keywords: First-order evolution equation, Schrödinger equation, nonlocal in time initial-boundary value problem, existence and uniqueness of solution, iteration algorithm, Sobolev spaces
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In this paper nonclassical initial-boundary value problems with non-local initial conditions for parabolic and Schrödinger type equations and systems, and their generalizations in abstract spaces are considered. The existence and uniqueness of solutions of nonlocal in time problems for first-order evolution equation and Schrödinger equation in abstract spaces is investigated. An algorithm of approximation of nonlocal problems by a sequence of classical problems is constructed and investigated. Applications of the obtained abstract results to initial-boundary value problems for parabolic and Schrödinger type equations and systems are presented.

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დროით არალოკალური ამოცანების გამოკვლევა პირველი რიგის ევოლუციური და შრედინგერის ტიპის განტოლებებისათვის [ka]