Семинар РМЦ ЮФУ. Лекция Gen­eral Solu­tion of the Div-​Curl System

В рамках еженедельного научно-​исследовательского семинара по анализу, дифференциальным уравнениям и математической физике РМЦ ЮФУ 20 сентября с 15:30 – 17:00 в ауд. 212 состоится лекция Briceyda B. Del­gado «Gen­eral Solu­tion of the Div-​Curl System».

Приглашаются преподаватели, научные сотрудники, аспиранты, студенты и все желающие. e-​mail: Этот адрес электронной почты защищён от спам-​ботов. У вас должен быть включен JavaScript для просмотра..

Regional math­e­mat­i­cal cen­ter of South­ern Fed­eral Uni­ver­sity is pleased to invite you to the Sem­i­nar on analy­sis, dif­fer­en­tial equa­tions and math­e­mat­i­cal physics, which will be held on 20 Sep­tem­ber 2018 at 15:30 in the room 212.

The title of the lec­ture: Gen­eral Solu­tion of the Div-​Curl Sys­tem. Lec­turer: Briceyda B. Delgado.

Abstract: In this talk we will give a brief intro­duc­tion to the non-​commutative alge­bra of quater­nions and we present dif­fer­ent results of the quater­nionic analy­sis.
We will give a com­plete solu­tion to the div-​curl sys­tem, that is we will recon­struct a vec­tor field w from its diver­gence g₀ and curl g [1], where the orig­i­nal data g₀ and g are L_p inte­grable func­tions in cer­tain bounded domains in R³.
This first order par­tial dif­fer­en­tial sys­tem gov­erns, for exam­ple, sta­tic elec­tro­mag­netic fields. In fact, Maxwell’s equa­tions con­sist of two simul­ta­ne­ous div-​curl sys­tems which describe how elec­tri­cal and mag­netic fields are gen­er­ated by charges and cur­rents together with their vari­a­tions.
The con­struc­tion of the solu­tion rely heav­ily on the com­po­nents oper­a­tors of the clas­si­cal Teodor­escu trans­form [2], as well as some prop­er­ties that allow to related them with the the­ory of har­monic func­tions. After that, we will con­struct an explicit inverse to the curl as well as the oper­a­tor that solves the div-​curl sys­tem above mentioned.

[1] B. B. Del­gado, R. M. Porter, “Gen­eral solu­tion of the inho­mo­ge­neous div– curl sys­tem and con­se­quences,” Advances in Applied Clif­ford Alge­bras (2017) 3015 – 3037.
[2] K. Gür­lebeck, K. Habetha, W. Sprößig, Holo­mor­phic Func­tions in the Plane and n-​dimensional Space. Birkhäuser, Basel (2008).