Evolution of the perturbation of a circle in the Stokes-Leibenson problem for the Hele-Shaw flow. Part II期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Evolution of the perturbation of a circle in the Stokes-Leibenson problem for the Hele-Shaw flow. Part II

Authors:

A S Demidov

Affiliation:

(1) Department Mechanics and Mathematics, Moscow State University, Russia, 119992

Abstract:

It is shown that an infinite-dimensional dynamical system of the form

$\begin{gathered} 2\left( {t + to} \right)\left( {\beta _1 \dot \beta _1 + r_1 (\beta )\dot \beta } \right) = \left( { - \beta _1^2 + 2\sum\limits_{j \geqslant 2} {\beta _j^2 } } \right) + s_1 (\beta ), \hfill \\ 2\left( {t + to} \right)\left( {\dot \beta _k + R_k (\beta )\dot \beta } \right) = \left( {k + 2} \right)\beta _k + s_k (\beta ),k \geqslant 2, \hfill \\ \end{gathered}$

studied for sufficiently small r ₁, s ₁, R _k, and S _k in the preceding part of this work Contemporary Mathematics and Its Applications, Vol. 2. Partial Differential Equations (2003), pp. 22–49] describes the evolution of the free boundary in the problem of the Hele-Shaw flow in the case where the pressure is constant on the free boundary (Leibenson condition). __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 24, Dynamical Systems and Optimization, 2005.

Keywords:

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