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SUMMARY:Symmetry analysis and exact solutions of a model describing viscou
 s fingering induced by a chemical reaction
DTSTART;VALUE=DATE-TIME:20260922T144000Z
DTEND;VALUE=DATE-TIME:20260922T144500Z
DTSTAMP;VALUE=DATE-TIME:20260914T052220Z
UID:indico-contribution-519@indico.bitp.kiev.ua
DESCRIPTION:Speakers: Vasyl' Davydovych (Institute of Mathematics\,  NAS o
 f Ukraine)\nWe study a mathematical model describing viscous fingering ind
 uced by the chemical reaction $A+B \\to C$\, introduced in [T. Gerard and 
 A. De Wit\, Phys. Rev. E\, 2009]. The model couples the concentrations of 
 the reactants\, $u(t\,x\,y)$ and $v(t\,x\,y)$\, and their product\, $w(t\,
 x\,y)$\, with the pressure $p(t\,x\,y)$ and the two-dimensional velocity f
 ield $U=(U_1\,U_2)$\, and is given by \n\n$ \\nabla\\cdot U=0\,  \\\n\\kap
 pa \\nabla p=-\\mu(w)U\,  \\\nu_t+ U\\cdot\\nabla u = d_1 \\triangle u-kuv
 \,  $\n$v_t+ U\\cdot\\nabla v = d_2 \\triangle v-kuv\,  \\\nw_t+U\\cdot\\n
 abla w = d_3 \\triangle w+kuv.$\n\nThe above system is investigated by mea
 ns of the classical Lie symmetry approach. A Lie symmetry classification i
 s obtained for different parameter cases\, and the resulting symmetries ar
 e used to construct exact solutions. In the case of radially symmetric str
 eam functions\, several families of exact solutions are derived. These sol
 utions make it possible to analyze the evolution of the reactant and produ
 ct concentrations in both space and time and provide an analytical descrip
 tion of the corresponding viscous-fingering dynamics.\n\nThe presented res
 ults were obtained in collaboration with R. M. Cherniha.\n\nhttps://indico
 .bitp.kiev.ua/event/18/contributions/519/
LOCATION:Bogolyubov Institute for Theoretical Physics Conference Hall
URL:https://indico.bitp.kiev.ua/event/18/contributions/519/
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