Abstract
We develop a method for solving problems with moving/evolving interfaces between heterogeneous media in Rd governed by parabolic partial differential equations. This technique can be applied in various engineering and biological applications. We assume a perfect contact at the evolving interface. The moving jump of material functions is tackled by the Reynolds transport theorem. The well-posedness of the setting is shown and the error estimates for time-discrete approximations are established in suitable function spaces.
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