Functional geometric method for solving free boundary problems for harmonic functions

DOI10.1070/RM2010v065n01ABEH004661zbMath1205.35343OpenAlexW2037837767MaRDI QIDQ3577758

A. S. Demidov

Publication date: 23 July 2010

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/rm2010v065n01abeh004661

zbMATH Keywords

harmonic functiontokamakfree boundarysteady flowHele-Shaw flownonlinear Riemann-Hilbert problemStokes-Leibenzon problem

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Asymptotic expansions of solutions to PDEs (35C20) Boundary value problems in the complex plane (30E25) Free boundary problems for PDEs (35R35) Ionized gas flow in electromagnetic fields; plasmic flow (76X05) Other free boundary flows; Hele-Shaw flows (76D27)

Related Items (6)

Stokes-Leibenson problem for Hele-Shaw flow: a critical set in the space of contours ⋮ Finding the coefficients in the new representation of the solution of the Riemann-Hilbert problem using the Lauricella function ⋮ Attractors-repellers in the space of contours in the Stokes-Leibenson problem for Hele-Shaw flows ⋮ Application of the multipole method to direct and inverse problems for the Grad-Shafranov equation with a nonlocal condition ⋮ The Lauricella hypergeometric function $F_D^{(N)}$, the Riemann–Hilbert problem, and some applications ⋮ On numerically implementable explicit formulas for the solutions to the 2D and 3D equations \(\operatorname{div}(\alpha(w)\nabla w)=0\) and \(\operatorname{div}(\beta\nabla w)=0\) with Cauchy data on an analytic boundary

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