Seminars: V. Zh. Sakbaev, Shiryaeva A., Nonlinear Schrödinger equation with delay and its regularization

SEMINARS


Seminar on nonlinear problems of partial differential equations and mathematical physics March 21, 2023 18:00, Moscow

Nonlinear Schrödinger equation with delay and its regularization V. Zh. Sakbaev^a, Shiryaeva A.^b ^a Keldysh Institute of Applied Mathematics ^b Gromov Flight Research Institute, Zhukovskii, Moscow region, Russia
Abstract: The report will be devoted to the properties of initial-boundary value problem for a nonlinear Schro¨dinger equation including terms with delay of time argument. The influence of the delay in the potential or source term on the changing of norm and energy is studied. The conditions of global existence or arising of gradient blow up phenomenon are obtained. The relation of the gradient blow up phenomenon with the self-focusing and the destruction of pure quantum state are described ( Grekhneva A.D., Sakbaev V.Zh. Dynamics of a Set of Quantum States Generated by a Nonlinear Liouville–von Neumann Equation// Comp. Math. Math. Phys. 2020. V. 60 (8). P. 1337-1347). Website: https://teams.microsoft.com/l/meetup-join/19%3ameeting_YzMyMjgxMjktYTY5ZC00M2Y4LWIzYTgtNDVjNTMxZTM1Njhh%40thread.v2/0?context=%7b%22Tid%22%3a%222ae95c20-c675-4c48-88d3-f276b762bf52%22%2c%22Oid%22%3a%2266c4b047-af30-41c8-9097-2039bac83cbc%22%7d