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The evolution of a two-phase Hele-Shaw problem, a Muskat problem, underassumption of a negligible surface tension is considered. We use the Schwarzfunction approach and allow the sinks and sources to be line distributions withdisjoint supports located in the exterior and the interior domains, a two-phasemother body. We give examples of exact solutions when the interface belongs toa certain family of algebraic curves, defined by the initial shape of theboundary, and the cusp formation does not occur.

Exact solutions to a Muskat problem with line distributions of sinks and sources