<div dir="ltr"><span style="color:rgb(80,0,80)"><div>Dear Colleagues!<br></div><br>You are cordially invited to the </span>
<span style="color:rgb(80,0,80)">Weekly Online</span> <span style="color:rgb(80,0,80)">Seminar “Analysis and Applied Mathematics” on<br><br></span>Date: Tuesday, December 20, 2022<span style="color:rgb(80,0,80)"><br><br>Time: 14.00-15.00 (Istanbul) = 13.00-14.00 (Ghent) = 17.00-18.00 (Almaty)<br><br>Zoom link: <a href="https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaH-lDaVYrN3l5bzJVQT09" target="_blank">https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaH-lDaVYrN3l5bzJVQT09</a>, Conference ID: 667 827 0445, Access code: 1<br><br></span>Speaker: Prof. Dr. Vsevolod Sakbaev <div>Keldysh Institute of Applied Mathematics Russian Academy of Science, Russian Federation.<div><div><br><div> Title:
On the Properties of Solutions of Nonlinear Schrodinger
Equation
</div><div>Abstract:We consider the transformation of the initial data space of the Cauchy problem
for the focusing nonlinear Schrodinger equation with power nonlinearity in potential ([1]-
[3]). Also we study properties of the initial-boundary value problem for a nonlinear
Schrodinger equation including terms with delay of time argument.
First, we prove the local existence for the Cauchy problem and for the initial problem. After
that we study the phenomenon of global existence as a solution of the Cauchy problem for
small powers of nonlinearity. In the case of large power of nonlinearity the phenomenon of
rise of a solution gradient blow up during a finite time is proven. In the last case we study qualitative properties of a solution when it approaches the boundary of its interval of existence.
Same properties are studied for the initial problem.
The relation of the gradient blow up phenomenon with the self-focusing and the destruction of the pure quantum state are described [2]. Moreover, we define a solution extension
through the moment of a gradient blow by means of the random process with values in the
set of pure quantum states. We show that this extension describes the destruction of a solution as the destruction of a pure quantum state and the transition from the set of pure quantum states into the set of mixed quantum states [3].</div><div><br></div><div> References: </div><div>[1] A.D. Grekhneva & V.Zh. Sakbaev, Dynamics of a Set of Quantum States Generated by
a Nonlinear Liouville–von Neumann Equation. Computational Mathematics & Mathematical Physics, 60:8 (2020), 1337-1347. </div><div>[2] L.S. Efremova, A.D. Grekhneva, V.Zh. Sakbaev, Phase flow generated by Cauchy
problem for nonlinear Schrodinger equation and dynamical mappings of quantum
states. Lobachevskii Journal of Mathematics, 40:10 (2019), 1455-1469. </div><div>[3] V.Zh. Sakbaev & A.D. Shiryaeva, Blow-Up of States in the Dynamics Given by the
Schrödinger Equation with a Power-Law Nonlinearity in the Potential. Differential
Equation, 58:4 (2022), 498-508.</div><div><br></div><div><span style="color:rgb(80,0,80)"><div>Abstracts and forthcoming talks can be found on our webpage<br><a href="https://sites.google.com/view/aam-seminars" target="_blank">https://sites.google.com/view/aam-seminars</a><br>With my best wishes</div></span></div></div></div><div><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div style="font-size:12.8px"><b style="font-size:12.8px">Prof. Dr. Allaberen Ashyralyev </b></div><div style="font-size:12.8px"><span style="font-size:small"><b>Department of Mathematics, Bahcesehir University, 34353, Istanbul, Turkey</b></span><b style="font-size:12.8px"> and </b><b style="font-size:12.8px">Near East University, Lefkoşa(Nicosia), Mersin 10 Turkey</b></div><div><div style="font-size:12.8px"><span style="font-size:12.8px"><b>Peoples' Friendship University of Russia (RUDN University),</b></span><b style="color:rgb(51,51,51);font-family:arial,helvetica,sans-serif;font-size:13px"> Ul Miklukho Maklaya 6, Moscow 117198, Russian Federation </b></div><div style="font-size:12.8px"><b style="font-size:12.8px">Institute of Mathematics and Mathematical Modelling, 050010, Almaty, Kazakhstan</b></div><div style="font-size:12.8px"><b style="font-size:12.8px">e-mail: <a href="mailto:allaberen.ashyralyev@neu.edu.tr" style="color:rgb(17,85,204)" target="_blank">allaberen.ashyralyev@eng.bau.edu.tr</a> and </b><b style="font-size:12.8px"><a href="mailto:aallaberen@gmail.com" style="color:rgb(17,85,204)" target="_blank">aallaberen@gmail.com</a> </b></div><div style="font-size:12.8px"><b style="font-size:12.8px"> </b><a href="http://akademik.bahcesehir.edu.tr/web/allaberenashyralyev" style="color:rgb(0,86,179);margin:0px;padding:0px;border:0px;font-stretch:inherit;font-size:14px;line-height:inherit;font-family:Roboto,sans-serif;vertical-align:baseline" target="_blank">http://akademik.bahcesehir.edu.tr/web/allaberenashyralyev</a></div><div><p class="MsoNormal"><a href="https://sites.google.com/view/aam-seminars" target="_blank">https://sites.google.com/view/aam-seminars</a></p></div><div><a href="https://content.sciendo.com/view/journals/ejaam/ejaam-overview.xml" target="_blank">https://content.sciendo.com/view/journals/ejaam/ejaam-overview.xml</a><br></div><div><font color="#1155cc"><span style="font-size:12.8px"><b><u><a href="http://icaam-online.org" target="_blank">icaam-online.org</a></u></b></span></font></div></div><div><font color="#1155cc"><span style="font-size:12.8px"><b><a href="https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1" target="_blank">https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1<br></a></b></span><br></font></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div>