Kochina and Hele-Shaw in modern mathematics, natural science and industry

Abstract A brief review of P. Ya. Kochina's studies, namely, her investigations of free-boundary problems for harmonic functions, is presented. Her ideas have had implications for many areas of quantitative science, including materials science, the environment, medicine and finance. Within mathematics, they have stimulated many new developments in the areas of complex analysis, asymptotic analysis, and partial differential equations with free boundaries.