Searching for analytic solutions of physically relevant non-linear partial differential equations

Nyomtatóbarát változatNyomtatóbarát változat
PhD típus: 
Fizikai Tudományok Doktori Iskola
Év: 
2023/2024/1
Témavezető: 
Név: 
Barna Imre Ferenc
Email cím: 
barna.imre@wigner.hu
Kutatóintézet/Tanszék: 
Wigner Fizikai Kutatóközpont
Beosztás: 
tudományos főmunkatárs
Tudományos fokozat: 
PhD
Konzulens: 
Név: 
Prof. Dr. Apagyi Barnabás
Email cím: 
apagyi@phy.bme.hu
Intézet: 
Fizikai Intézet
Beosztás: 
Címzetes Egyetemi Tanár
Tudományos fokozat: 
MTA Doktora
Leírás: 
Searching for analytic solutions of physically relevant non-linear partial differential equations 
 
There are numerous fields in physics which deal with highly non-linear phenomena, 
and take place in space and time decribed by non-linear partial differential equations (PDE) 
such as wave phenomena, transport processes like fluid dynamics, plasma physics, high-energy 
physics or grativation. There is no existing general mathematical theory of non-linear PDEs, 
however there are some trial functions (Ansätze) like self-similar solutions, traveling 
waves which give us physically relevant reasonable solutions helping to get a deeper 
insight into the internal properties of such systems. 
In the last decades we investigated numerous PDEs, most of them were problems from 
viscous hydrodynamics [1], but difusion [2], non-linear electrodynamics [3] or 
dark fluid [4] were addressed as well. 
The candidate should have a solid knowledge in basic theoretical physics and 
ordinary differential equations. We can offer problems in fluid dynamics -- which is under our 
present interest --, but the research field of could be slightly changed and defined 
together with the PhD candidate. 
For background information see papers at: http://www.kfki.hu/~barnai
 
[1]  I.F. Barna, G. Bognár, L. Mátyás and K. Hriczó,
"Self-similar analysis of the time-dependent compressible and incompressible boundary
layer including heat condution"
Journal of Thermal Analysis and Calorimetry 147 (2022) 13625
[2] I.F. Barna and l. Mátyás
"Advanced Analytic Self-Similar Solutions of Regular and Irregular Diffusion Equations"
Mathematics  10, (2022)  3281
[3] I.F. Barna
"Self-similar shock wave solutions of the non-linear Maxwell equations"
Laser Phys. 24, (2014) 086002 
[4]   I.F. Barna, M.A. Pocsai and G.G. Barnaföldi
"Self-similar solutions of a gravtitating dark fluid"
Mathematics 10 (2022) 3220
 
Elvárások: 

<p>Solid knowledge of basic theoretical physics and ordinary differential equations Good communication skills in English Basic knowledge of the Latex, Maple and Mathematica softwares</p>

Munkahely neve: 
Wigner FK
Munkahely címe: 
Konkoly Thege Miklós út 29 - 33, Budapest, 1121