Two main existence theorems are proved for two nonstandard systems ofparabolic initial-boundary value problems. The systems are based on the "$ \phi$-$ \eta $-$ \theta $ model" proposed by Kobayashi [RIMS Kokyuroku, 1210(2001), 68-77] as a phase-field model of planar grain boundary motion underisothermal solidification. Although each of the systems has specificcharacteristics and mathematical difficulties, the proofs of the main theoremsare based on the time discretization method by means of a common approximatingproblem. As a consequence, we provide a uniform solution method for a widescope of parabolic systems associated with the $ \phi $-$ \eta $-$ \theta $model.
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