an:06973057
Zbl 1402.76092
Dolgikh, T. F.; Zhukov, M. Yu.; Shiryaeva, E. V.
The solution of elliptic equations with periodic data for zone electrophoresis problem
RU
Vestn. Voronezh. Gos. Univ., Ser. Fiz. Mat. 2017, No. 2, 85-96 (2017).
00372372
2017
j
76M25 65L10 76R10
quasilinear elliptic equations; spatially periodic initial data; hodograph method; zonal electrophoresis
Summary: The hodograph method based on the conservation laws used for construct of implicit form solution for a system of first order quasilinear elliptic equations. These equations describe the model of zone electrophoresis. We construct the Riemann-Green function which allows us to obtain the solution in implicit form. Analytical-numerical method for recovery of an explicit solution on the level lines implicit solutions is proposed. This method is based on the construction of the Cauchy problem for systems of ordinary differential equations whose solution allows us to obtain an explicit solution in parametric form for the original problem. Examples of solutions with a variety of periodic data is studied.