Free boundary problem

A free boundary problem determines both a field and part of its domain boundary. A glacier terminus, for example, separates positive ice thickness from bare bed. Mass conservation, nonnegative thickness, a rule for ice ablation only where ice exists, and suitable interface or entropy solution conditions are needed; a formal zero of one characteristic branch alone need not give the selected physical boundary.

A drying front separates a positive liquid layer from a region where its thickness is zero. Its position is an unknown boundary determined with the wet-region solution. At a continuous zero-height front, a jump balance alone need not fix its speed; the vanishing-depth profile and removal law can supply that information. Source terms representing evaporation or infiltration must respect nonnegative water availability in the dry region.